Theoretical and Numerical Investigation of the Finite Cell Method

We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lamé problems in one, two as well as three dimensions. Several numerical examples in one and two dimensions including a well-known benchmark problem from linear elasticity confirm the results of the mathematical analysis of the finite cell method.

Subjects

Adaptive quadrature

Finite cell method

Finite element method

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Theoretical and Numerical Investigation of the Finite Cell Method