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Some Remarks on Generalized Finite Element Methods (GFEM) in Solid Mechanics

After a short introduction to Generalized Finite Element Methods (GFEM) for two-dimensional triangular elements, a technique is presented to impose Dirichlet-type boundary conditions to global higher order GFEM ansatz spaces. The convergence rates of h-, p-, hp-and enriched p-versions of the GFEM are discussed with respect to singularities. The method is applied to a two dimensional Poisson model problem and the global errors measured in energy norm are compared.