Optimal Order $L^2$ Error Estimate of SDFEM on Shishkin Triangular Meshes for Singularly Perturbed Convection-Diffusion Equations

DOI10.1137/15M101035XzbMath1342.65223MaRDI QIDQ5739966

Min Yang, Jin Zhang, Xiao-Wei Liu

Publication date: 7 July 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical experimentserror estimatestreamline diffusion finite element methodShishkin triangular meshsingularly perturbed convection-diffusion equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (26)

Supercloseness of linear streamline diffusion finite element method on Bakhvalov-type mesh for singularly perturbed convection-diffusion equation in 1D ⋮ Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers ⋮ Analysis of finite element method in balanced norms for two-parameter singularly perturbed problems ⋮ Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D ⋮ Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: vertex-cell interpolation ⋮ Stability and error analysis of a fully-discrete numerical method for system of 2D singularly perturbed parabolic PDEs ⋮ Uniform convergence of a weak Galerkin method for singularly perturbed convection-diffusion problems ⋮ Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in <scp>2D</scp> ⋮ Supercloseness and post-processing of finite element method in a balanced norm for singularly perturbed reaction-diffusion equation ⋮ Streamline diffusion finite element method for a singularly perturbed problem with an interior layer on Shishkin mesh ⋮ A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction-convection-diffusion equations ⋮ Supercloseness in a balanced norm of finite element methods on Shishkin and Bakhvalov–Shishkin rectangular meshes for reaction–diffusion problems ⋮ Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh in 2D ⋮ Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems ⋮ Optimal order of uniform convergence for finite element method on Bakhvalov-type meshes ⋮ Supercloseness of weak Galerkin method on Bakhvalov-type mesh for a singularly perturbed problem in 1D ⋮ Uniform supercloseness of Galerkin finite element method for convection-diffusion problems with characteristic layers ⋮ Convergence in \(L^{2}\) norm of the SDFEM on a Shishkin triangular mesh for problems with characteristic layers ⋮ Galerkin finite element methods for convection-diffusion problems with exponential layers on Shishkin triangular meshes and hybrid meshes ⋮ Finite element method on Shishkin mesh for a singularly perturbed problem with an interior layer ⋮ Supercloseness of linear finite element method on Bakhvalov-type meshes for singularly perturbed convection-diffusion equation in 1D ⋮ Supercloseness of continuous interior penalty methods on Shishkin triangular meshes and hybrid meshes for singularly perturbed problems with characteristic layers ⋮ Convergence and supercloseness in a balanced norm of finite element methods on Bakhvalov-type meshes for reaction-diffusion problems ⋮ Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh ⋮ Supercloseness of continuous interior penalty method for convection-diffusion problems with characteristic layers ⋮ Uniform stability of the SUPG method for the evolutionary convection-diffusion-reaction equation

Cites Work

• Unnamed Item
• Unnamed Item
• Using rectangularqpelements in the SDFEM for a convection-diffusion problem with a boundary layer
• Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers
• A novel exponentially fitted triangular finite element method for an advection-diffusion problem with boundary layers
• A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem
• Layer-adapted meshes for convection-diffusion problems
• Pointwise estimates of the SDFEM for convection-diffusion problems with characteristic layers
• Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers
• Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection-diffusion problem
• Numerical solution of saddle point problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Layer-Adapted Grids for Singular Perturbation Problems
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• An Analysis of Smoothing Effects of Upwinding Strategies for the Convection-Diffusion Equation
• Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems
• Pointwise error estimates of the bilinear SDFEM on Shishkin meshes
• Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities
• Finite element superconvergence on Shishkin meshes for convection-diffusion problems with corner singularities
• Superconvergence on a hybrid mesh for singularly perturbed problems with exponential layers
• The SDFEM on Shishkin meshes for linear convection-diffusion problems
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem

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