Skip to main content

Research Repository

Advanced Search

The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method

Houston, Paul; Muga, Ignacio; Roggendorf, Sarah; van der Zee, Kristoffer

The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method Thumbnail


Authors

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths

Ignacio Muga

Sarah Roggendorf

KRISTOFFER VAN DER ZEE KG.VANDERZEE@NOTTINGHAM.AC.UK
Professor of Numerical Analysis &computational Applied Mathematics



Abstract

While it is classical to consider the solution of the convection-diffusion-reaction equation in the Hilbert space H10(Ω), the Banach Sobolev space W1,q0(Ω), 1 less than ∞ , is more general allowing more irregular solutions. In this paper we present a well-posedness theory for the convection-diffusion-reaction equation in the W1,q0(Ω)-W1,q′0(Ω) functional setting, 1q+1q′=1. The theory is based on directly establishing the inf-sup conditions. Apart from a standard assumption on the advection and reaction coefficients, the other key assumption pertains to a subtle regularity requirement for the standard Laplacian. An elementary consequence of the well-posedness theory is the stability and convergence of Galerkin’s method in this setting, for a diffusion-dominated case and under the assumption of W1,q′-stability of the H10-projector.

Journal Article Type Article
Acceptance Date Apr 30, 2019
Online Publication Date Jun 27, 2019
Publication Date Jun 27, 2019
Deposit Date May 19, 2019
Publicly Available Date Jun 28, 2020
Journal Computational Methods in Applied Mathematics
Print ISSN 1609-4840
Electronic ISSN 1609-9389
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 19
Issue 3
Pages 503-522
DOI https://doi.org/10.1515/cmam-2018-0198
Keywords Applied Mathematics; Numerical Analysis; Computational Mathematics
Public URL https://nottingham-repository.worktribe.com/output/2064818
Publisher URL https://www.degruyter.com/view/j/cmam.2019.19.issue-3/cmam-2018-0198/cmam-2018-0198.xml

Files





You might also like



Downloadable Citations