Well-posedness and finite element approximation of mixed dimensional partial differential equations
Artikel i vetenskaplig tidskrift, 2024

In this article, a mixed dimensional elliptic partial differential equation is considered, posed in a bulk domain with a large number of embedded interfaces. In particular, well-posedness of the problem and regularity of the solution are studied. A fitted finite element approximation is also proposed and an a priori error bound is proved. For the solution of the arising linear system, an iterative method based on subspace decomposition is proposed and analyzed. Finally, numerical experiments are presented and rapid convergence using the proposed preconditioner is achieved, confirming the theoretical findings.

Mixed dimensional partial differential equation

Finite element method

Preconditioner

Subspace decomposition

A priori error analysis

Författare

Fredrik Hellman

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Axel Målqvist

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Malin Mosquera

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

BIT Numerical Mathematics

0006-3835 (ISSN) 1572-9125 (eISSN)

Vol. 64 1 2

Ämneskategorier

Beräkningsmatematik

DOI

10.1007/s10543-023-01001-w

Mer information

Senast uppdaterat

2024-01-12