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Well-Posedness and Finite Element Approximation of Mixed Dimensional Partial Differential Equations by Hellman, Fredrik; Målqvist, Axel; Mosquera, Malin is a scholarly article available to read on EtoBox.

What is Well-Posedness and Finite Element Approximation of Mixed Dimensional Partial Differential Equations about?

We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose a fitted finite element approximation and prove an a priori error bound. For the solution of the arising linear system we propose and analyze an iterative method based on subspace decomposition. Finally, we present numerical experiments and achieve rapid convergence using the proposed preconditioner, confirming our theoretical findings.

Author

Hellman, Fredrik; Målqvist, Axel; Mosquera, Malin

Published

2022

Language

EN