Numerical Methods for Partial Differential Equations

Article	Citations
Dual least‐squares finite element method with stabilization	68
New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes	28
Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment	26
A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes	23
A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows	17
Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in 2D	15
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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	14
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Convergence and optimality of an adaptive modified weak Galerkin finite element method	13
The TRUNC element in any dimension and application to a modified Poisson equation	12
Parameter‐robust mixed element method for poroelasticity with Darcy‐Forchheimer flow	11
An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications	11
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A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations	10
Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant	10
A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation	9
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations	9
Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations	8
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow	8
Efficient and accurate temporal second‐order numerical methods for multidimensional multi‐term integrodifferential equations with the Abel kernels	8
Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem	8
Experimental convergence rate study for three shock‐capturing schemes and development of highly accurate combined schemes	8
A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation	7

Determining a time‐varying potential in time‐fractional diffusion from observation at a single point	7
Block preconditioners for energy stable schemes of magnetohydrodynamics equations	7
Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system	7
Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation	7
Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems	7
An a priori error analysis of a type III thermoelastic problem with two porosities	7
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem	6
Convergence analysis of expanded mixed virtual element methods for nonlocal problems	6
Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients	6
Numerical approximations for the nonlinear time fractional reaction–diffusion equation	6
Linearized and decoupled structure‐preserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations	6
A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations	6
Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian	6
Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations	6
Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer	6
Inverse problems for discontinuous Dirac operator with eigenparameter dependent boundary and transmission conditions	6
Spectral approximation for optimal control problems governed by first bi‐harmonic equation	6
A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate	6
The divergence‐free nonconforming virtual element method for the Navier–Stokes problem	6
Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations	5
Discrete null field equation methods for solving Laplace's equation: Boundary layer computations	5
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Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models	5
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Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids	5
An adaptive mesh refinement method based on a characteristic‐compression embedded shock wave indicator for high‐speed flows	5
A modified walk‐on‐sphere method for high dimensional fractional Poisson equation	5
A kernel‐based method for solving the time‐fractional diffusion equation	5
A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation	5
Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise	5
Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number	5
Error estimates of an operator‐splitting finite element method for the time‐dependent natural convection problem	5
Time filters and spurious acoustics in artificial compression methods	5
An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation	5
A Finite Element Method for a Nonlinear Magnetostatic Problem in Terms of Scalar Potentials	5
Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation	4
A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type	4
A combined compact finite difference scheme for solving the acoustic wave equation in heterogeneous media	4
Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator	4
A semi‐relativistic time‐fractional Vlasov–Maxwell code for numerical simulation based on circular polarization and Landau damping instability	4
On the sparse multiscale representation of 2‐D Burgers equations by an efficient algorithm based on multiwavelets	4
Nitsche's method for a Robin boundary value problem in a smooth domain	4
A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations	4
A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems	4
Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases	4
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Highly accurate difference schemes for time‐nonlocal Schrodinger type problems	3
Numerical analysis of a corrected Smagorinsky model	3
Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media	3
Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations	3

Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem	3
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Using radial basis function‐generated quadrature rules to solve nonlocal continuum models	3
Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant	3
Numerical analysis of two decoupled algorithms for a parabolic two domain problem	3
A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation	3
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves	3
A Legendre spectral‐Galerkin method for fourth‐order problems in cylindrical regions	3
Convergence analysis of the splitting method to the nonlinear heat equation	3
Integrated radial basis functions to simulate modified anomalous sub‐diffusion equation	3
A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations	3
A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions	3
Numerical approximation of the optimal control of a population dynamics model	3
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A heat transfer problem with exponential memory and the associated thermal stresses	3
Two‐level methods based on the Arrow–Hurwicz iteration for the steady incompressible magnetohydrodynamic system	3
Energy stability of exponential time differencing schemes for the nonlocal Cahn‐Hilliard equation	3
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Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric ra	2
A parareal exponential integrator finite element method for semilinear parabolic equations	2
Higher order weak Galerkin methods for the Navier–Stokes equations with large Reynolds number	2
A Finite Volume Element Scheme Modified With Second‐Order Upwind Fractional Step of Three‐Dimensional Semiconductor Device Transient Behavior and Its Convergence Analysis	2
Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps	2
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A spectral collocation method for a nonlinear multidimensional Volterra integral equation	2
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A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations	2
A minimax algorithm based on Newton's method and an application for finding multiple solutions of p‐area problems	2
Operator splitting for the fractional Korteweg‐de Vries equation	2
A class of one‐parameter alternating direction implicit methods for two‐dimensional wave equations with discrete and distributed time‐variable delays	2
A mixed element analysis of the Biot's model with Darcy–Forchheimer flow	2
A novel convenient finite difference method for shallow water waves derived by fifth‐order Kortweg and De‐Vries‐type equation	2
A flux‐based HDG method	2
An efficient flux‐variable approximation scheme for Darcy's flow	2
Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation	2
A linear finite difference scheme with error analysis designed to preserve the structure of the 2D Boussinesq paradigm equation	2
A kernel‐based pseudo‐spectral method for multi‐term and distributed order time‐fractional diffusion equations	2
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On numerical study of constrained coupled shape optimization problems based on a new shape derivative method	2
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Special Issue Dedicated to Professor Qiang Du on the Occasion of His 60th Birthday	2
Retraction	2
Mixed convection of ferrofluids in a square enclosure with obstacles: Effect of iso‐perimetric shapes	2
Kernel Compensation Method for Maxwell Eigenproblem in Photonic Crystals With Mimetic Finite Difference Discretizations	2
Finite element analysis of the singularly perturbed parabolic reaction‐diffusion problems with retarded argument	2
L1‐type finite element method for time‐fractional diffusion‐wave equations on nonuniform grids	2
Optimal error estimates of a decoupled finite element scheme for the unsteady inductionless MHD equations	2
Two‐order superconvergence for a weak Galerkin method on rectangular and cuboid grids	2
Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem	2
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme	2
Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions	2
Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study	2
A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions	2
A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes	2
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Two Numerical Schemes Via an Auxiliary Function for Nonlocal Problems With Integrable Kernels	2
Analysis and application of a local discontinuous Galerkin method for the electromagnetic concentrator model	2
A study of distributed‐order time fractional diffusion models with continuous distribution weight functions	2
Convective thermal conditions and the thermophoretic effect's impacts on a hybrid nanofluid over a moving thin needle	2
P1$$ {P}_1 $$‐nonconforming quadrilateral finite element space with periodic boundary conditions: Part II. Application to the nonconforming heterogeneous multiscale method	1
Controllability of nonlinear Hilfer fractional Langevin dynamical system	1
Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system	1
Compressive‐Sensing‐Assisted Mixed Integer Optimization for Dynamical System Discovery With Highly Noisy Data	1
Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime	1
Structure‐Preserving Approximation of the Cahn‐Hilliard‐Biot System	1
Three dimensional high order finite volume element schemes for elliptic equations	1
Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion	1
High order accurate method for the numerical solution of the second order linear hyperbolic telegraph equation	1
A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation	1
Primal‐dual active set algorithm for valuating American options under regime switching	1
Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods	1
Analysis of sparse recovery for Legendre expansions using envelope bound	1
Conforming finite element method for the time‐fractional nonlinear stochastic fourth‐order reaction diffusion equation	1
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise	1
Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form	1
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Numerical analysis for a class of coupled system of singularly perturbed time‐dependent convection‐diffusion equations with a discontinuous source term	1
Improved error bounds on a time splitting method for the nonlinear Schrödinger equation with wave operator	1
Positivity‐preserving scheme without separated method for 2D convection–diffusion equations on polygonal meshes	1
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Strong optimal error estimates of discontinuous Galerkin method for multiplicative noise driving nonlinear SPDEs	1
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Solving Multi‐Term Time‐Fractional Diffusion Equations Using a High‐Order Fractional Finite Difference Scheme Accompanied by Neural Network Techniques	1
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A three‐step Oseen‐linearized finite element method for incompressible flows with damping	1
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations	1
Efficient, linearized high‐order compact difference schemes for nonlinear parabolic equations I: One‐dimensional problem	1
Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system	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 wavelet collocation method for fractional Black–Scholes equations by subdiffusive model	1
Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density	1
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TheBDF2 FDMfor the fourth‐order equations with the multi‐termR‐Lfractional integral kernels	1
Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization	1
Compactness results for a Dirichlet energy of nonlocal gradient with applications	1
Numerical methods for scattering problems from multi‐layers with different periodicities	1
Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions	1
Orthogonal polynomial bases in the mixed virtual element method	1
Numerical solution of convected wave equation in free field using artificial boundary method	1
Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation	1
A numerical scheme for the optimal control of groundwater pollution	1
Pulsatile Darcy flow of water‐based thermally radiative carbon nanotubes between two concentric cylinders	1
Layer‐parallel training of residual networks with auxiliary variable networks	1
An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling	1
A virtual element method‐based positivity‐preserving conservative scheme for convection–diffusion problems on polygonal meshes	1
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Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators	1
On the application of a Krylov subspace spectral method to poroacoustic shocks in inhomogeneous gases	1
A C0 interior penalty method for the phase field crystal equation	1
Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element	1
A systematic study on weak Galerkin finite element method for second‐order parabolic problems	1
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Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations	1
On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations	1
Discontinuous Galerkin finite element method for dynamic viscoelasticity models of power‐law type	1
Two‐grid finite element method on grade meshes for time‐fractional nonlinear Schrödinger equation	1
Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations	0
A new ϕ‐FEM approach for problems with natural boundary conditions	0
Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media	0
Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation	0
Decoupled modified characteristic finite element method for the time‐dependent Navier–Stokes/Biot problem	0
A discontinuous least squares finite element method for the Helmholtz equation	0
A type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method	0
An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity	0
On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations	0
A variable‐step high‐order scheme for time‐fractional advection‐diffusion equation with mixed derivatives	0
A Mixed Finite Element Method for Vibration Equations of Structurally Damped Beam and Plate	0
Learning parameters of a system of variable order fractional differential equations	0
Convergence of first‐order finite volume method based on exact Riemann solver for the complete compressible Euler equations	0
Numerical study of conforming space‐time methods for Maxwell's equations	0
Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass	0
An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations	0
Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint	0
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A positivity preserving high‐order finite difference method for compressible two‐fluid flows	0
Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature	0
Virtual element method for elliptic bulk‐surface PDEs in three space dimensions	0
Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model	0
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization	0
Numerical solution of the boundary value problem of elliptic equation by Levi function scheme	0
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Iteration acceleration methods for solving three‐temperature heat conduction equations on distorted meshes	0
Exponential time difference methods with spatial exponential approximations for solving boundary layer problems	0
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Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves	0
Error estimates for completely discrete FEM in energy‐type and weaker norms	0
Numerical approximation of solutions of the equations of quasistatic electroporoelasticity	0
On the optimality of voronoi‐based column selection	0
A new high order hybrid WENO scheme for hyperbolic conservation laws	0
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow	0
On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation	0
Multiphysics mixed finite element method with Nitsche's technique for Stokes‐poroelasticity problem	0
Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein–Gordon–Schrödinger equations	0
Robust Error Estimates for Second‐Order Stabilization Finite Element Method for Navier–Stokes Equations With Small Viscosity and Nonsmooth Initial Data	0
A C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients	0
Mathematical model for the novel coronavirus (2019‐nCOV) with clinical data using fractional operator	0
Uniform and optimal error estimates of a nested Picard integrator for the nonlinear Schrödinger equation with wave operator	0
Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media	0
Error bound of the multilevel fast multipole method for 3‐D scattering problems	0
A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations	0
High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method	0
On the convergence of 2D P4+$$ {P}_{4+} $$ triangular and 3D P6+$$ {P}_{6+} $$ tetrahedral divergence‐free finite elements	0
Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws	0
On the compact difference scheme for the two‐dimensional coupled nonlinear Schrödinger equations	0
Partial differential integral equation model for pricing American option under multi state regime switching with jumps	0
Error estimate of a finite element method for an optimal control problem with corner singularity using the stress intensity factor	0
Magnetohydrodnamics nanofluid flow of shaped nanoparticles over a porous stretching wall and slip effect	0
An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint	0
An a posteriori error analysis for an augmented discontinuous Galerkin method applied to Stokes problem	0
Unconditionally stable exponential time differencing schemes for the mass‐conserving Allen–Cahn equation with nonlocal and local effects	0
Richardson extrapolation method for solving the Riesz space fractional diffusion problem	0
A two‐grid discontinuous Galerkin method for an incompressible miscible displacement problem	0