Uniform mesh approximation to nonsmooth solutions of a singularly perturbed convection-diffusion equation in a rectangle

DOI10.1134/S0012266109070052zbMath1176.65119OpenAlexW2086829443WikidataQ115252735 ScholiaQ115252735MaRDI QIDQ1033662

Vladimir B. Andreev

Publication date: 6 November 2009

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266109070052

zbMATH Keywords

convergenceDirichlet problemsingular perturbationfinite difference methodconvection-diffusion equationsecond order elliptic equationShishkin piecewise uniform mesh

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (7)

Convergence of the numerical solution of the initial-boundary value problem for a heat equation with a corner singularity in derivatives of the solution ⋮ An optimal a priori error estimate in the maximum norm for the Il'in scheme in 2D ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem ⋮ Parameter-uniform error estimate for the implicit four-point scheme for a singularly perturbed heat equation with corner singularities ⋮ Scaled discrete derivatives of singularly perturbed elliptic problems ⋮ Estimating the smoothness of the regular component of the solution to a one-dimensional singularly perturbed convection-diffusion equation

Cites Work

• A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes
• A technique to prove parameter-uniform convergence for a singularly perturbed convection-diffusion equation
• Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an $L$-shaped domain
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• 10.1007/s11470-008-1007-5
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem

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