SFB 1313 Publication "Flux-mortar mixed finite element methods with multipoint flux approximation"

New SFB 1313 publication, published in Computer Methods in Applied Mechanics and Engineering. The work has been developed within the SFB 1313 research project Z02.

"Flux-mortar mixed finite element methods with multipoint flux approximation"

Authors

• Wietse M. Boon (University of Stuttgart, SFB 1313 internal research project I-01)
• Dennis Gläser (University of Stuttgart, SFB 1313 internal research project I-03)
• Rainer Helmig (University of Stuttgart, SFB 1313 research project A02)
• Ivan Yotov (University of Pittsburgh, USA, SFB 1313 Mercator Fellow and external partner, research project A02)

Abstract

The flux-mortar mixed finite element method was recently developed in Boon et al. (2022) for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux approximation as the subdomain discretization. The subdomain problems involve solving positive definite cell-centered pressure systems. The normal flux on the subdomain interfaces is the mortar coupling variable, which plays the role of a Lagrange multiplier to impose weakly continuity of pressure. We present well-posedness and error analysis based on reformulating the method as a mixed finite element method with a quadrature rule. We develop a non-overlapping domain decomposition algorithm for the solution of the resulting algebraic system that reduces it to an interface problem for the flux-mortar, as well as an efficient interface preconditioner. A series of numerical experiments is presented illustrating the performance of the method on general grids, including applications to flow in complex porous media.