Work

An optimally convergent Fictitious Domain method for interface problems

Year: 2024

Type: article

Abstract: We introduce a novel Fictitious Domain (FD) unfitted method for interface problems associated with a second-order elliptic linear differential operator, that achieves optimal convergence without the need for adaptive mesh refinements nor enrichments of the Finite Element spaces. The key aspect of the proposed method is that it extends the solution into the fictitious domain in a way that ensures high global regularity. Continuity of the solution across the interface is enforced through a boundary Lagrange multiplier. The subdomains coupling, however, is not achieved by means of the duality pairing with the Lagrange multiplier, but through an L2 2 product with the H1 1 Riesz representative of the latter, thus avoiding gradient jumps across the interface. Thanks to the enhanced regularity, the proposed method attains an increase, with respect to standard FD methods, of up to one order of convergence in energy norm. The Finite Element formulation of the method is presented, followed by its analysis. Numerical tests on a model problem demonstrate its effectiveness and its superior accuracy compared to standard unfitted methods.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2024.117327

Author: Francesco Regazzoni

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,660