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Theoretical and numerical investigation of the finite cell method

Abstract : 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 Lame 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.
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Monique Dauge, Alexander Düster, Ernst Rank. Theoretical and numerical investigation of the finite cell method. Journal of Scientific Computing, Springer Verlag, 2015, 65 (3), pp.1039-1064. ⟨10.1007/s10915-015-9997-3⟩. ⟨hal-00850602v3⟩

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