Analysis of a Modified Second-Order Mixed Hybrid $BDM_1$ Finite Element Method for Transport Problems in Divergence Form
Brunner F, Fischer J, Knabner P (2016)
Publication Status: Published
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: SIAM PUBLICATIONS
Book Volume: 54
Pages Range: 2359-2378
Journal Issue: 4
DOI: 10.1137/15M1035379
Abstract
We prove optimal second order convergence of a modified lowest-order Brezzi-Douglas-Marini (BDM1) mixed finite element scheme for advection-diffusion problems in divergence form. If advection is present, it is known that the total flux is approximated only with first-order accuracy by the classical BDM1 mixed method, which is suboptimal since the same order of convergence is obtained if the computationally less expensive Raviart-Thomas (RT0) element is used. The modification that was first proposed by Brunner et al. [Adv. Water Res., 35 (2012), pp. 163-171] is based on the hybrid problem formulation and consists in using the Lagrange multipliers for the discretization of the advective term instead of the cellwise constant approximation of the scalar unknown.
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
Germany (DE)How to cite
APA:
Brunner, F., Fischer, J., & Knabner, P. (2016). Analysis of a Modified Second-Order Mixed Hybrid $BDM_1$ Finite Element Method for Transport Problems in Divergence Form. SIAM Journal on Numerical Analysis, 54(4), 2359-2378. https://dx.doi.org/10.1137/15M1035379
MLA:
Brunner, Fabian, Julian Fischer, and Peter Knabner. "Analysis of a Modified Second-Order Mixed Hybrid $BDM_1$ Finite Element Method for Transport Problems in Divergence Form." SIAM Journal on Numerical Analysis 54.4 (2016): 2359-2378.
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