Numerical approximation of mixed dimensional partial differential equations
Licentiate thesis, 2023
From finite element methods, one obtains large linear systems that need to be solved, either directly or via an iterative method. We discuss an iterative method, which converges faster when using a preconditioner on the linear system. The preconditioner that we utilise is based on domain decomposition.
In Paper I, we consider this kind of partial differential equation posed on a domain with interfaces, and show existence and uniqueness of a solution. We state and prove a regularity result in two dimensions. Further, we propose a fitted finite element approximation and derive error estimates to show conver- gence. We also present a preconditioner based on domain decomposition that we use together with an iterative method, and analyse the convergence. Finally, we perform numerical experiments that confirm the theoretical findings.
mixed dimensional partial differential equation
preconditioner
a priori error analysis
Finite element method
subspace decomposition
Author
Malin Mosquera
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
https://arxiv.org/abs/2212.14387
Subject Categories
Computational Mathematics
Mathematical Analysis
Publisher
University of Gothenburg
Pascal, Chalmers tvärgata 3
Opponent: Karl Larsson, universitetslektor vid Umeå universitet, Umeå, Sverige