Convergence and superconvergence analysis of finite element methods on graded meshes for singularly and semisingularly perturbed reaction-diffusion problems

DOI10.1016/j.cam.2007.08.025zbMath1155.65093OpenAlexW2064877583MaRDI QIDQ939539

Shao-Chun Chen, Guo-Qing Zhu

Publication date: 22 August 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.08.025

zbMATH Keywords

singular perturbationerror estimatesnumerical experimentsfinite elementsuperconvergencegraded meshessemisingular perturbation

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 (6)

Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Energy-norm and balanced-norm supercloseness error analysis of a finite volume method on Shishkin meshes for singularly perturbed reaction-diffusion problems ⋮ Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for semisingularly perturbed reaction–diffusion problems ⋮ Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems ⋮ Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes

Cites Work

• Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type
• Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem
• Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem
• Finite element approximation of convection diffusion problems using graded meshes
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• Steady-state convection-diffusion problems
• Layer-Adapted Grids for Singular Perturbation Problems
• Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids
• Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction-diffusion problems
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