Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form Journal Article


Author(s): Brunner, Fabian; Fischer, Julian; Knabner, Peter
Article Title: Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form
Affiliation
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.
Keywords: Advection-diffusion problem; Mixed finite element methods; Optimal convergence; Suboptimal convergence
Journal Title: SIAM Journal on Numerical Analysis
Volume: 54
Issue 4
ISSN: 1095-7170
Publisher: Society for Industrial and Applied Mathematics  
Date Published: 2016-01-01
Start Page: 2359
End Page: 2378
DOI: 10.1137/15M1035379
Open access: no
IST Austria Authors
  1. Julian Fischer
    13 Fischer
Related IST Austria Work