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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2018

17-11-2017

Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection–Diffusion Equations

Authors: Yana Di, Hehu Xie, Xiaobo Yin

Published in: Journal of Scientific Computing | Issue 1/2018

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Abstract

We propose a numerical strategy to generate a sequence of anisotropic meshes and select appropriate stabilization parameters simultaneously for linear SUPG method solving two dimensional convection-dominated convection–diffusion equations. Since the discretization error in a suitable norm can be bounded by the sum of interpolation error and its variants in different norms, we replace them by some terms which contain the Hessian matrix of the true solution, convective field, and the geometric properties such as directed edges and the area of triangles. Based on this observation, the shape, size and equidistribution requirements are used to derive corresponding metric tensor and stabilization parameters. Numerical results are provided to validate the stability and efficiency of the proposed numerical strategy.
previous article Flux-Conservative Hermite Methods for Simulation of Nonlinear Conservation Laws
next article Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems

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Metadata
Title
Anisotropic Meshes and Stabilization Parameter Design of Linear SUPG Method for 2D Convection-Dominated Convection–Diffusion Equations
Authors
Yana Di
Hehu Xie
Xiaobo Yin
Publication date
17-11-2017
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0610-9

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