Numerical approximation of mixed dimensional partial differential equations
Licentiatavhandling, 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
Författare
Malin Mosquera
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
https://arxiv.org/abs/2212.14387
Ämneskategorier
Beräkningsmatematik
Matematisk analys
Utgivare
Göteborgs universitet
Pascal, Chalmers tvärgata 3
Opponent: Karl Larsson, universitetslektor vid Umeå universitet, Umeå, Sverige