Numerical Methods for Partial Differential Equations

Article	Citations
Error Estimates of a Space‐Time Spectral Method for Nonlinear Klein–Gordon Equation With Unknown Coefficients	73
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	52
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	21
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	20
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	20
An Extended Virtual Element Method for the Shallow Shell Model	19
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Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	15
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	14
Convergence analysis of the splitting method to the nonlinear heat equation	14
A Modified Brinkman Penalization Fictitious Domain Method for the Unsteady Navier‐Stokes Equations	13
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	13
A parareal exponential integrator finite element method for semilinear parabolic equations	13
Numerical Analysis of the Quadratic Spline Collocation Method and Averaged L1 Scheme on Graded Mesh for Nonlinear Time‐Fractional Fourth‐Order Reaction‐Diffusion Problem	13
A Linearized Conservative Compact Difference Scheme for the BBM–Burgers Equation With Numerical Simulations	13
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Jacobi Convolution Series for Petrov–Galerkin Scheme and General Fractional Calculus of Arbitrary Order Over Finite Interval	12
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	11
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	11
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	11
A Local RBF‐Based Differential Quadrature Method for Solving the Gray–Scott Model	10
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	10
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	10

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Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	9
A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	9
On the Stability Barrier of Hermite Type Discretizations of Advection Equations	9
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	9
A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model	8
A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model	8
Uniform Error Estimates of an Energy‐Preserving Exponential Wave Integrator for the Nonlinear SchröDinger Equation With Wave Operator	8
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A Systematic Stability Analysis of Explicit Runge–Kutta Discontinuous Galerkin Methods for Maxwell'S Equations	8
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Finite Difference Method for Nonlinear Damped Viscoelastic Euler‐Bernoulli Beam Model	8
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	7
Modeling Anomalous Diffusion With Riesz Fractional Derivatives: Applications to Pattern Formation	7
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	7
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	7
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	7
Optimal L 2 Error Quadratic Serendipity Finite Volume Element Methods for Diffusion Equations on Polygonal Meshes	7
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	7
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	7
A Spectral Galerkin Approximation for Second‐Order Non‐Selfadjoint Steklov Eigenvalue Problems in Complex Domains	6
A Macro‐Bubble Enriched Divergence‐Free Finite Element on Quadrilateral Meshes	6
P1$$ {P}_1 $$–Nonconforming quadrilateral finite element space with periodic boundary conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis	6
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	6
A multistep collocation method for solving advection equations with delay	6
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WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh	6
A C0$$ {C}^0 $$ Finite Element Algorithm for the Sixth Order Problem With Simply Supported Boundary Conditions	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	6
An Adaptive Time Filter Algorithm for the 2D/3D Unsteady Triple‐Porosity Stokes Model Arising in Super‐Hydrophobic Proppant Modification in Hydraulic Fracturing Systems	6
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	6
Artificial Compressibility Method for the Incompressible Navier–Stokes Equations With Variable Density	6
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	6
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	5
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A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema	5
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SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification	5
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations	5
A Numerical Approach for (2+1)D Saturable Nonlinear Schrödinger Equations With Generalized Loss	5
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	5
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
The TRUNC element in any dimension and application to a modified Poisson equation	5
Inf‐Sup Stable Non‐Conforming Finite Elements on Tetrahedra With Second‐ and Third‐Order Accuracy	5
A flux‐based HDG method	5

An Efficient Probabilistic Scheme for the Exit Time Probability of α‐Stable Lévy Process	4
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	4
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation	4
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	4
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	4
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	4
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A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	4
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
A Posteriori Error‐Driven Space‐Time Adaptive FEM for Accurate Avascular Tumor and Drug Interaction Modeling	4
Some Discontinuous Galerkin Schemes for Korteweg‐De Vries Equations: Error Estimates and Application	4
Dissipation‐Dispersion Analysis of Fully Discrete Implicit Discontinuous Galerkin Methods and Application to Stiff Hyperbolic Problems	4
Retraction	3
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
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A Flexible Derivation Approach for the Numerical Solution of Partial Differential Equations	3
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Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	3
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	3
Error analysis of a fully discrete projection method for magnetohydrodynamic system	3
Regularization Methods Based on a Priori Information for Backward Inhomogeneous Caputo Time‐Fractional Parabolic Equation	3
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Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	3
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A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	3
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	3
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	3
Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	3
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves	3
A C0 interior penalty method for the phase field crystal equation	3
Two‐Level Implicit High Accuracy Method in Exponential Form for 2D Quasi‐Linear Parabolic Equations on Irrational Domain	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
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Deriving Locally Conservative Fluxes From High‐Order Finite Element Solutions by Solving a Constrained Minimization Problem	3
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	3
Unfitted mixed finite element methods for elliptic interface problems	3
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A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	3
A Multi‐Domain Space‐Time Spectral Collocation Method for the Huxley Equation	2
Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	2
Second‐Order Least‐Squares Fitting Relaxation Method for Ginzburg‐Landau‐Schrödinger Equation	2
On the Numerical Performance of Extrapolation‐Projection Linear L1 Scheme for Time‐Fractional Allen‐Cahn Dynamics	2
On the optimality of voronoi‐based column selection	2
A note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	2
Numerical solution of convected wave equation in free field using artificial boundary method	2
Numerical Method and Analysis for the Coupled Sine‐Gordon Equations on Unbounded Domains	2
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
A Linear Variable‐Step Embedded ETD Scheme With Uniform‐in‐Time Stability for the 2D Navier Stokes Equations	2
An a priori error analysis of a type III thermoelastic problem with two porosities	2
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New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	2
Dual least‐squares finite element method with stabilization	2
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	2
Pseudostress‐Based Velocity Formulation for the Stokes‐Brinkman‐Type Eigenvalue Problem: A Priori and a Posteriori Error Analysis	2
A priori error estimates of two monolithic schemes for Biot's consolidation model	2
Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods	2
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	2
Superconvergent Meshless Collocation Method for Nonlinear Neutral Delay‐Reaction‐Diffusion Equation	2
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Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	2
Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation	2
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	2
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	2
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	2
A well‐balanced and entropy stable scheme for a reduced blood flow model	2
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	2

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A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	2
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	2
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A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
The Landau–Lifshitz–Bloch Equation With Spin Diffusion: Global Strong Solution and Finite Element Approximation	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	2
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	2
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Optimal Control of the Viscous Wave Equation via the Pontryagin Maximum Principle	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
On the SAV‐DG method for a class of fourth order gradient flows	2
A Simple Weak Galerkin Method for the Brinkman Equations on Nonconvex Polytopal Meshes	2
A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	2
Improved Error Estimates on Time‐Splitting Method for the Space Fractional Klein–Gordon–Schrödinger Equation With the Small Coupling Constant	2
Mixed Shifted Generalized Laguerre–Fourier Spectral Method for Exterior Problem of Fisher Equation	2
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
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Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	2
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
A Linearly Implicit and Structure‐Preserving Scheme for the Ginzburg–Landau–Schrödinger Equation	1
A simplified primal‐dual weak Galerkin finite element method for Fokker–Planck‐type equations	1
A Structure‐Informed Framework for Solving Time‐Dependent Partial Differential Equations With Neural Networks	1
A New Minimization Solver for Computing the Ground States of Bose–Einstein Condensates	1
A fourth‐order accurate numerical method for the distributed‐order Riesz space fractional diffusion equation	1
Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids	1
Controllability of nonlinear Hilfer fractional Langevin dynamical system	1
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	1
A Hybrid WENO Method for Hyperbolic Conservation Laws on the Polygonal Mesh With Mixed Elements	1
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	1
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Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	1
On the Stabilizer‐Free Immersed Weak Galerkin FEM: A Posteriori Error Estimation in a Non‐Conforming Framework	1
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	1
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions	1
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	1
Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect	1
A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model	1
Maximum Convergence of a Novel High‐Precision Conservative Compact Difference Scheme for the Coupled Nonlinear Schrödinger (CNLS) Equations	1
An error analysis of the finite element method of the Stokes equations with parameter based on the singular function expansion	1
A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations	1
Primal‐dual active set algorithm for valuating American options under regime switching	1
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	1
A Modified Dynamic Diffusion Finite Element Method With Optimal Convergence Rate for Convection‐Diffusion‐Reaction Equations	1
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Nitsche's method for a Robin boundary value problem in a smooth domain	1
A numerical scheme for the optimal control of groundwater pollution	1
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	1
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	1
Three dimensional high order finite volume element schemes for elliptic equations	1
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1
A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary condition	1
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation	1
Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density	1
A kernel‐based method for solving the time‐fractional diffusion equation	1
Fast ADI Finite Difference Method for Two‐Dimensional Space‐Fractional Diffusion Equations on Nonuniform Spatial Grids	1
Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization	1
A Priori Error Estimates for H(curl)$$ \mathbf{H}\left(\operatorname{curl}\right) $$ and H(div)$$ \mathbf{H}\left(\operatorname{div}\right) $$‐Elliptic Interface Problems: Least‐Squares Weak Galerkin	1
Structure‐Preserving Approximation of the Cahn‐Hilliard‐Biot System	1
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	1
Towards hybrid two‐phase modelling using linear domain decomposition	1
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	1
An Efficient and Robust Weak Galerkin Scheme for Solving the 2D/3D H(curl;Ω)‐Elliptic Interface Problems With High‐Order Elements	1
On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation	1
Optimal L2‐Norm Error Estimates for Steady and Unsteady Maxwell Equations Using Skeletal Discontinuous Galerkin Methods	1
Unconditional H2$$ {H}^2 $$‐stability of the Euler implicit/explicit SAV‐based scheme for the 2D Navier–Stokes equations with smooth or nonsmooth initial data	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1
A Study on Spatially Loaded Time‐Fractional Diffusion Equation: Well‐Posedness, Discretization, and Simulation	1
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	1
A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis	1
Efficient Lie Group Algorithms for the Complex Swift‐Hohenberg Model: Stability and Energy Conservation	1
Clustering‐Based Low Rank Approximation Method	1
Mixed Finite Element Methods for the Nonlinear Stochastic Elastodynamics Equations With Multiplicative Noise	1
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	1
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	1
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	1
Jacobi‐Galerkin Spectral Method for the Fractional Diffusion Equation	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
High‐Order Weak Galerkin Finite Element Method for Analysis and Simulation of Nonlinear Wave Propagation in Homogeneous Media	1
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	1
An efficient flux‐variable approximation scheme for Darcy's flow	1
Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier–Stokes equations	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	1
Linearized compact difference schemes applied to nonlinear variable coefficient parabolic equations with distributed delay	1