An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems

Anita Hansbo (1) , Peter Hansbo (2)

1 Department of Informatics and Mathematics
2 Department of Applied Mechanics

In this paper we propose a method for the finite element solution of elliptic interface problem, using an approach due to Nitsche. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. Further, we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples.

Domaines: Mathématiques [math]

Anita Hansbo, Peter Hansbo. An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Computer Methods in Applied Mechanics and Engineering, 2002, 191 (47-48), pp. 5537-5552. ⟨10.1016/S0045-7825(02)00524-8⟩. ⟨hal-01352903⟩