The Finite Cell Method with Least Squares Stabilized Nitsche Boundary Conditions

TL;DR

This paper introduces a novel finite cell method that employs a least squares stabilized symmetric Nitsche approach for Dirichlet boundary conditions, resulting in a positive definite system with favorable stability and error properties.

Contribution

It combines least squares stabilized Nitsche boundary conditions with finite cell methods, providing a symmetric positive definite matrix without extra fill-in and establishing theoretical error and stability bounds.

Findings

The method produces a symmetric positive definite stiffness matrix.

A priori error estimates are established.

Condition number bounds are derived.

Abstract

We apply the recently developed least squares stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions to the finite cell method. The least squares stabilized Nitsche method in combination with finite cell stabilization leads to a symmetric positive definite stiffness matrix and relies only on elementwise stabilization, which does not lead to additional fill in. We prove a priori error estimates and bounds on the condition numbers.