A uniformly convergent weak Galerkin finite element method on Shishkin mesh for 1d convection-diffusion problem

DOI10.1007/s10915-020-01345-3zbMath1452.65365OpenAlexW3093586144MaRDI QIDQ2211743

Shenglan Xie, Peng Zhu

Publication date: 12 November 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-020-01345-3

zbMATH Keywords

convection-diffusion equationsingularly perturbed problemShishkin meshweak Galerkin finite element method

Mathematics Subject Classification ID

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) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (11)

Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D ⋮ Uniform convergence of a weak Galerkin method for singularly perturbed convection-diffusion problems ⋮ Uniform convergent modified weak Galerkin method for convection-dominated two-point boundary value problems ⋮ Supercloseness of weak Galerkin method for a singularly perturbed convection-diffusion problem in 2D ⋮ An \textit{hp} weak Galerkin FEM for singularly perturbed problems ⋮ Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations ⋮ A dimensional-splitting weak Galerkin finite element method for 2D time-fractional diffusion equation ⋮ Uniform convergence of finite element method on Bakhvalov-type triangular mesh for a singularly perturbed problem featuring exponential layers ⋮ Supercloseness of weak Galerkin method on Bakhvalov-type mesh for a singularly perturbed problem in 1D ⋮ Optimal order uniform convergence in energy and balanced norms of weak Galerkin finite element method on Bakhvalov-type meshes for nonlinear singularly perturbed problems ⋮ Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms

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