Uniformly convergent high order finite element solutions of a singularly perturbed reaction-diffusion equation using mesh equidistribution

DOI10.1016/S0168-9274(01)00049-6zbMath0988.65053MaRDI QIDQ5948558

John A. Mackenzie, G. Beckett

Publication date: 26 June 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

Galerkin methodsingular perturbationnumerical examplesboundary value problemsreaction-diffusion equationgrid refinementFinite element methodsUniform convergence

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Robust adaptive computation of a one-dimensional \(\mathbb Q\)-tensor model of nematic liquid crystals, A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems, A brief survey on numerical methods for solving singularly perturbed problems, A posteriori error analysis for finite element solution of one-dimensional elliptic differential equations using equidistributing meshes, Adaptivity with moving grids, Unconditionally stable high-order time integration for moving mesh finite difference solution of linear convection–diffusion equations, Computational solution of two-dimensional unsteady PDEs using moving mesh methods

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