A Numerical Assessment of Finite Element Discretizations for Convection-Diffusion-Reaction Equations Satisfying Discrete Maximum Principles-Reference-Cited by-同舟云学术

A Numerical Assessment of Finite Element Discretizations for Convection-Diffusion-Reaction Equations Satisfying Discrete Maximum Principles

Published:2022-09-30 Issue:0 Volume:0 Page:
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

John Volker¹^ORCID,Knobloch Petr²^ORCID,Pártl Ondřej³

Affiliation:

1. Weierstrass Institute for Applied Analysis and Stochastics , Leibniz Institute in Forschungsverbund Berlin e.V. (WIAS), Mohrenstr. 39, 10117; and Department of Mathematics and Computer Science, Freie Universität of Berlin, Arnimallee 6, 14195 Berlin , Germany

2. Department of Numerical Mathematics , Faculty of Mathematics and Physics , Charles University , Sokolovská 83, 18675 Praha 8 , Czech Republic

3. Weierstrass Institute for Applied Analysis and Stochastics , Leibniz Institute in Forschungsverbund Berlin e. V. (WIAS), Mohrenstr. 39, 10117 Berlin , Germany

Abstract

Abstract Numerical studies are presented that investigate finite element methods satisfying discrete maximum principles for convection-diffusion-reaction equations. Two linear methods and several nonlinear schemes, some of them proposed only recently, are included in these studies, which consider a number of two-dimensional examples. The evaluation of the results examines the accuracy of the numerical solutions with respect to quantities of interest, like layer widths, and the efficiency of the simulations.

Funder

Grantová Agentura České Republiky

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0125/pdf

Reference42 articles.

1. M. Augustin, A. Caiazzo, A. Fiebach, J. Fuhrmann, V. John, A. Linke and R. Umla, An assessment of discretizations for convection-dominated convection-diffusion equations, Comput. Methods Appl. Mech. Engrg. 200 (2011), no. 47–48, 3395–3409.

2. K. Baba and M. Tabata, On a conservative upwind finite element scheme for convective diffusion equations, RAIRO Anal. Numér. 15 (1981), no. 1, 3–25.

3. R. E. Bank, W. M. Coughran, Jr. and L. C. Cowsar, The finite volume Scharfetter–Gummel method for steady convection diffusion equations, Comput. Vis. Sci. 1 (1998), no. 3, 123–136.

4. G. R. Barrenechea, E. Burman and F. Karakatsani, Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes, Numer. Math. 135 (2017), no. 2, 521–545.

5. G. R. Barrenechea, V. John and P. Knobloch, Analysis of algebraic flux correction schemes, SIAM J. Numer. Anal. 54 (2016), no. 4, 2427–2451.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Finite Element Methods Respecting the Discrete Maximum Principle for Convection-Diffusion Equations;SIAM Review;2024-02

2. Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations;SIAM Journal on Scientific Computing;2023-08-03

3. An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes;Numerical Algorithms;2023-04-04

4. On algebraically stabilized schemes for convection–diffusion–reaction problems;Numerische Mathematik;2022-10-19