Analysis of an upwind-mixed hybrid finite element method for transport problems
Brunner F, Radu AF, Knabner P (2014)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2014
Journal
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 52
Pages Range: 83-102
Journal Issue: 1
DOI: 10.1137/130908191
Abstract
We prove optimal order convergence of an upwind-mixed hybrid finite element scheme for linear parabolic advection-diffusion-reaction problems. It was introduced in [Radu et al., Adv. Water Resources, 34(2011), pp. 47-61] and is based on an Euler-implicit mixed hybrid finite element discretization of the problem in fully mass conservative form using the Raviart-Thomas mixed finite element of lowest order on triangular meshes. Optimal order convergence in time and space is obtained for the fully discrete formulation. The scheme provides the same order of convergence as the standard upwind-mixed method, while it is more efficient since a local elimination of variables is possible with our choice of the upwind weights. The theoretical findings are sustained by a numerical experiment. © 2014 Society for Industrial and Applied Mathematics.
Authors with CRIS profile
Fabian Brunner
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Peter Knabner
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Involved external institutions
Norway (NO)How to cite
APA:
Brunner, F., Radu, A.F., & Knabner, P. (2014). Analysis of an upwind-mixed hybrid finite element method for transport problems. SIAM Journal on Numerical Analysis, 52(1), 83-102. https://doi.org/10.1137/130908191
MLA:
Brunner, Fabian, Adrian Florin Radu, and Peter Knabner. "Analysis of an upwind-mixed hybrid finite element method for transport problems." SIAM Journal on Numerical Analysis 52.1 (2014): 83-102.
BibTeX: Download