An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes-Reference-Cited by-同舟云学术

An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes

Published:2017-03 Issue:03 Volume:27 Page:525-548
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Barrenechea Gabriel R.¹,John Volker²³,Knobloch Petr⁴

Affiliation:

1. Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK

2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

3. Department of Mathematics and Computer Science, Free University of Berlin, Arnimallee 6, 14195 Berlin, Germany

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

Abstract

This work is devoted to the proposal of a new flux limiter that makes the algebraic flux correction finite element scheme linearity and positivity preserving on general simplicial meshes. Minimal assumptions on the limiter are given in order to guarantee the validity of the discrete maximum principle, and then a precise definition of it is proposed and analyzed. Numerical results for convection–diffusion problems confirm the theory.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202517500087

Reference31 articles.

1. An assessment of discretizations for convection-dominated convection–diffusion equations

2. Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization

3. On Monotonicity-Preserving Stabilized Finite Element Approximations of Transport Problems

4. On discrete maximum principles for discontinuous Galerkin methods

5. Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes

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