A Higher Order Isoparametric Fictitious Domain Method for Level Set Domains

TL;DR

This paper introduces a higher order fictitious domain method combining Nitsche's technique and facet stabilization with an isoparametric finite element space based on a specialized mesh transformation, achieving high accuracy for level set domains.

Contribution

It develops a novel higher order fictitious domain approach using a specialized mesh transformation and stabilization techniques for improved accuracy in level set domain problems.

Findings

Method achieves high accuracy and robustness.

Numerical examples confirm theoretical analysis.

Reduces numerical integration complexity.

Abstract

We consider a new fictitious domain approach of higher order accuracy. To implement Dirichlet conditions we apply the classical Nitsche method combined with a facet-based stabilization (ghost penalty). Both techniques are combined with a higher order isoparametric finite element space which is based on a special mesh transformation. The mesh transformation is build upon a higher order accurate level set representation and allows to reduce the problem of numerical integration to problems on domains which are described by piecewise linear level set functions. The combination of this strategy for the numerical integration and the stabilized Nitsche formulation results in an accurate and robust method. We introduce and analyze it and give numerical examples.