A Multimesh Finite Element Method for the Stokes Problem
Paper in proceedings, 2020

The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous–discontinuous function space with interface conditions enforced by means of Nitsche’s method. In this contribution, we consider the Stokes problem as a first step towards flow applications. The multimesh formulation leads to so called cut elements in the underlying meshes close to overlaps. These demand stabilization to ensure coercivity and stability of the stiffness matrix. We employ a consistent least-squares term on the overlap to ensure that the inf-sup condition holds. We here present the method for the Stokes problem, discuss the implementation, and verify that we have optimal convergence.

Unfitted mesh

CutFEM

FEM

Multimesh

Non-matching mesh

Nitsche

Author

August Johansson

SINTEF Digital

Simula Research Laboratory

Mats Larson

Umeå University

Anders Logg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Lecture Notes in Computational Science and Engineering

1439-7358 (ISSN)

Vol. 132 189-198

19th International Conference on Finite Elements in Flow Problems, FEF 2017
Rome, Italy,

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.1007/978-3-030-30705-9_17

More information

Latest update

4/16/2020