On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations

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Date
2011
Volume
1656
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

Finite element and finite difference discretizations for evolutionary convection-diffusion-reaction equations in two and three dimensions are studied which give solutions without or with small under- and overshoots. The studied methods include a linear and a nonlinear FEM-FCT scheme, simple upwinding, an ENO scheme of order 3, and a fifth order WENO scheme. Both finite element methods are combined with the Crank--Nicolson scheme and the finite difference discretizations are coupled with explicit total variation diminishing Runge--Kutta methods. An assessment of the methods with respect to accuracy, size of under- and overshoots, and efficiency is presented, in the situation of a domain which is a tensor product of intervals and of uniform grids in time and space. Some comments to the aspects of adaptivity and more complicated domains are given. The obtained results lead to recommendations concerning the use of the methods.

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Keywords
Time-dependent convection-diffusion-reaction equations, under- and overshoots, FEMFCT schemes, ENO schemes, WENO schemes
Citation
John, V., & Novo, J. (2011). On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations (Vol. 1656). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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