Another uniform convergence analysis technique of some numerical methods for parabolic singularly perturbed problems

DOI10.1016/j.camwa.2015.04.006zbMath1443.65118OpenAlexW2071939925MaRDI QIDQ2006161

J. C. Jorge, Carmelo Clavero

Publication date: 8 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.04.006

zbMATH Keywords

singular perturbationuniform convergencediscrete maximum principlesspecial meshes

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Cites Work

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• Layer-adapted meshes and FEM for time-dependent singularly perturbed reaction-diffusion problems
• Uniform fourth order difference scheme for a singular perturbation problem
• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• Finite element analysis of exponentially fitted lumped schemes for time- dependent convection-diffusion problems
• A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems
• A high order uniformly convergent alternating direction scheme for time dependent reaction-diffusion singularly perturbed problems
• Fitted Numerical Methods For Singular Perturbation Problems
• Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
• A Globally Uniformly Convergent Finite Element Method for a Singularly Perturbed Elliptic Problem in Two Dimensions
• A uniformly convergent alternating direction HODIE finite difference scheme for 2D time-dependent convection-diffusion problems
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Approximation of the solutions of singularly perturbed boundary-value problems with a parabolic boundary layer
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Difference Methods for Singular Perturbation Problems
• A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions
• Uniform High-Order Difference Schemes for a Singularly Perturbed Two-Point Boundary Value Problem
• Asymptotic Analysis of a Singular Perturbation Problem
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• Adaptive Lagrange–Galerkin methods for unsteady convection-diffusion problems
• A parameter robust numerical method for a two dimensional reaction-diffusion problem
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem

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