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

F. Brunner, J.L. Fischer, P. Knabner, SIAM Journal on Numerical Analysis 54 (2016) 2359–2378.

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Journal Article | Published
Author
Brunner, Fabian; Fischer, Julian LIST Austria ; Knabner, Peter
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.
Publishing Year
Date Published
2016-01-01
Journal Title
SIAM Journal on Numerical Analysis
Volume
54
Issue
4
Page
2359 - 2378
IST-REx-ID

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Brunner F, Fischer JL, Knabner P. Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form. SIAM Journal on Numerical Analysis. 2016;54(4):2359-2378. doi:10.1137/15M1035379
Brunner, F., Fischer, J. L., & Knabner, P. (2016). Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form. SIAM Journal on Numerical Analysis, 54(4), 2359–2378. https://doi.org/10.1137/15M1035379
Brunner, Fabian, Julian L Fischer, and Peter Knabner. “Analysis of a Modified Second-Order Mixed Hybrid BDM1 Finite Element Method for Transport Problems in Divergence Form.” SIAM Journal on Numerical Analysis 54, no. 4 (2016): 2359–78. https://doi.org/10.1137/15M1035379.
F. Brunner, J. L. Fischer, and P. Knabner, “Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form,” SIAM Journal on Numerical Analysis, vol. 54, no. 4, pp. 2359–2378, 2016.
Brunner F, Fischer JL, Knabner P. 2016. Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form. SIAM Journal on Numerical Analysis. 54(4), 2359–2378.
Brunner, Fabian, et al. “Analysis of a Modified Second-Order Mixed Hybrid BDM1 Finite Element Method for Transport Problems in Divergence Form.” SIAM Journal on Numerical Analysis, vol. 54, no. 4, Society for Industrial and Applied Mathematics , 2016, pp. 2359–78, doi:10.1137/15M1035379.

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