The finite cell method with least squares stabilized Nitsche boundary conditions

Karl Larsson; Stefan Kollmannsberger; Ernst Rank; Mats G. Larson

doi:10.1016/j.cma.2022.114792

The finite cell method with least squares stabilized Nitsche boundary conditions

Karl Larsson, Stefan Kollmannsberger, Ernst Rank, Mats G. Larson

Engineering and Design

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16 Scopus citations

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.

Original language	English
Article number	114792
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	393
DOIs	https://doi.org/10.1016/j.cma.2022.114792
State	Published - 1 Apr 2022

Keywords

A priori error estimates
Dirichlet conditions
Finite cell method
Nitsche's method

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10.1016/j.cma.2022.114792

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title = "The finite cell method with least squares stabilized Nitsche boundary conditions",

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.",

keywords = "A priori error estimates, Dirichlet conditions, Finite cell method, Nitsche's method",

author = "Karl Larsson and Stefan Kollmannsberger and Ernst Rank and Larson, {Mats G.}",

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AU - Kollmannsberger, Stefan

AU - Rank, Ernst

AU - Larson, Mats G.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - 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.

AB - 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.

KW - A priori error estimates

KW - Dirichlet conditions

KW - Finite cell method

KW - Nitsche's method

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DO - 10.1016/j.cma.2022.114792

M3 - Article

AN - SCOPUS:85126527849

SN - 0045-7825

VL - 393

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 114792

ER -

The finite cell method with least squares stabilized Nitsche boundary conditions

Abstract

Keywords

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