Numerical Methods for Partial Differential Equations

Article	Citations
	69
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	31
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	30
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	18
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	17
Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	14
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	14
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	13
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	13
Convergence analysis of the splitting method to the nonlinear heat equation	12
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	12
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	12
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	12
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A parareal exponential integrator finite element method for semilinear parabolic equations	11
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	11
Analysis of sparse recovery for Legendre expansions using envelope bound	10
A three‐step Oseen‐linearized finite element method for incompressible flows with damping	10
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	10
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A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	9
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A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	8
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	8
Numerical Analysis of the Quadratic Spline Collocation Method and Averaged L1 Scheme on Graded Mesh for Nonlinear Time‐Fractional Fourth‐Order Reaction‐Diffusion Problem	8
Error analyses on block‐centered finite difference schemes for distributed‐order non‐Fickian flow	8
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A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization	8
Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters	7
Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise	7
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	7
A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems	7
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A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	7
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations	7
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A positivity‐preserving and energy stable scheme for a quantum diffusion equation	7
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
A multistep collocation method for solving advection equations with delay	6
Optimal control problem of various epidemic models with uncertainty based on deep reinforcement learning	6
Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint	6
Multiscale modeling and analysis for some special additive noises driven stochastic partial differential equations	6
Efficient quadrature rules for finite element discretizations of nonlocal equations	6
The analysis of the solution of the Burgers–Huxley equation using the Galerkin method	6
Fourier spectral methods with exponential time differencing for space‐fractional partial differential equations in population dynamics	6
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	6
Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions	6
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	6
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A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	6
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	6
Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation	6
A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients	6
A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the Rosenau‐Korteweg de Vries equation	6
The TRUNC element in any dimension and application to a modified Poisson equation	5
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	5
P1$$ {P}_1 $$–Nonconforming quadrilateral finite element space with periodic boundary conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis	5
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	5
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	5
Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	5
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Block preconditioners for energy stable schemes of magnetohydrodynamics equations	5
A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations	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 discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
A flux‐based HDG method	4
Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	4
Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	4

A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	4
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	4
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	4
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
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	4
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A C0 interior penalty method for the phase field crystal equation	3
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	3
Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	3
Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations	3
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Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations	3
Retraction	3
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	3
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	3
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	3
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem	3
Second‐order efficient nonlinear filter stabilization for high Reynolds number flows	3
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On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	3
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	3
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Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	3
Error analysis of a fully discrete projection method for magnetohydrodynamic system	2
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	2
Semi‐analytic time differencing methods for singularly perturbed initial value problems	2
Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	2
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	2
Numerical solution of convected wave equation in free field using artificial boundary method	2
Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
An a priori error analysis of a type III thermoelastic problem with two porosities	2
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	2
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters	2
Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	2
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
Dual least‐squares finite element method with stabilization	2
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	2
On the numerical approximation of Boussinesq/Boussinesq systems for internal waves	2
Stability and error analysis of a splitting method using Robin–Robin coupling applied to a fluid–structure interaction problem	2
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	2
A note on a posteriori error analysis for dual mixed methods with mixed boundary conditions	2
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	2
Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation	2
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model	2
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	2
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	2
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	2
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	2
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	2
Unfitted mixed finite element methods for elliptic interface problems	2
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	2
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	2
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Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments	2
A heat transfer problem with exponential memory and the associated thermal stresses	2
A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions	2
Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations	2
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	2
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A priori error estimates of two monolithic schemes for Biot's consolidation model	2
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion	2
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	2
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	2
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	2
Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws	2
Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation	2
Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme	2
On the compact difference scheme for the two‐dimensional coupled nonlinear Schrödinger equations	2
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High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	2
A meshfree radial basis function method for simulation of multi‐dimensional conservation problems	2

A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations	1
Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids	1
An efficient flux‐variable approximation scheme for Darcy's flow	1
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	1
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	1
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Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	1
Numerical approximation of solutions of the equations of quasistatic electroporoelasticity	1
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	1
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	1
Fully discrete error analysis of first‐order low regularity integrators for the Allen‐Cahn equation	1
Three dimensional high order finite volume element schemes for elliptic equations	1
Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions	1
Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn–Hilliard–Darcy system	1
A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy	1
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind	1
A numerical scheme for the optimal control of groundwater pollution	1
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Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	1
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	1
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	1
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	1
A kernel‐based method for solving the time‐fractional diffusion equation	1
A staggered cell‐centered finite element method for Stokes problems with variable viscosity on general meshes	1
A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems	1
On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation	1
Numerical analysis of a corrected Smagorinsky model	1
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	1
A Novel ADI‐Weak Galerkin Method for Singularly Perturbed Two‐Parameter 2D Parabolic Pdes	1
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	1
Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	1
Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation	1
A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions	1
On the optimality of voronoi‐based column selection	1
A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations	1
Analysis of two fully discrete spectral volume schemes for hyperbolic equations	1
A well‐balanced and entropy stable scheme for a reduced blood flow model	1
Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density	1
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Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	1
Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms	1
Nitsche's method for a Robin boundary value problem in a smooth domain	1
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	1
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	1
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	1
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier–Stokes equations	1
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A new ϕ‐FEM approach for problems with natural boundary conditions	1
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A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis	1
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation	1
Structure‐Preserving Approximation of the Cahn‐Hilliard‐Biot System	1
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	1
Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters	1
Controllability of nonlinear Hilfer fractional Langevin dynamical system	1
Novel superconvergence analysis of anisotropic triangular FEM for a multi‐term time‐fractional mixed sub‐diffusion and diffusion‐wave equation with variable coefficients	1
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	1
Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation	1
Collocation method for one dimensional nonlocal diffusion equations	1
On the SAV‐DG method for a class of fourth order gradient flows	1
Primal‐dual active set algorithm for valuating American options under regime switching	1
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	1
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	1
Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	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
Time dependent subgrid multiscale stabilized finite element analysis of fully coupled transient Navier–Stokes‐transport model	1