A simple yet effective modification to the standard finite element method is presented in this paper.The basic idea is an extension of a partial differential equationbeyond the physical domain of computation up to theboundaries of an embedding domain, which can easier bemeshed. If this extension is smooth, the extended solutioncan be well approximated by high order polynomials. Thisway, the finite element mesh can be replaced by structuredor unstructured cells embedding the domain where classicalh- or p-Ansatz functions are defined. An adequate scheme fornumerical integration has to be used to differentiate betweeninside and outside the physical domain, very similar to strategiesused in the level set method. In contrast to earlier works,e.g., the extended or the generalized finite element method,no special interpolation function is introduced for enrichmentpurposes. Nevertheless, when using p-extension, themethodshows exponential rate of convergence for smooth problemsand good accuracy even in the presence of singularities.The formulation in this paper is applied to linear elasticityproblems and examined for 2D cases, although the conceptsare generally valid.
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