Optimally convergent high-order X-FEM for problems with voids and inclusions
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Cita com:
hdl:2117/17031
Tipus de documentText en actes de congrés
Data publicació2012
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
Solution of multiphase problems shows discontinuities across the material interfaces,
which are usually weak. Using the eXtended Finite Element Method (X-FEM), these
problems can be solved even for meshes that do not match the geometry. The basic idea is to
enrich the interpolation space by means of a ridge function that is able to reproduce the discontinuity
inside the elements. This approach yields excellent results for linear elements, but fails
to be optimal if high-order interpolations are used.
In this work, we propose a formulation that ensures optimal convergence rates for bimaterial
problems. The key idea is to enrich the interpolation using a Heaviside function that allows the
solution to represent polynomials on both sides of the interface and, provided the interface is
accurately approximated, it yields optimal convergence rates. Although the interpolation is
discontinuous, the desired continuity of the solution is imposed modifying the weak form.
Moreover, in order to ensure optimal convergence, an accurate description of the interface
(which also defines an integration rule for the elements cut by the interface) is needed. Here, we
comment on different options that have been successfully used to integrate high-order X-FEM
elements, and describe a general algorithm based on approximating the interface by piecewise
polynomials of the same degree that the interpolation functions.
CitacióSala, E.; Fernandez, S.; Huerta, A. Optimally convergent high-order X-FEM for problems with voids and inclusions. A: European Congress on Computational Methods in Applied Sciences and Engineering. "ECCOMAS 2012: 6th European Congress on Computational Methods in Applied Sciences and Engineering. Programme book of abstracts, September 10-14, 2012, Vienna, Austria". 2012, p. 1-14.
ISBN978-3-9502481-9-7
Versió de l'editorhttp://cataleg.upc.edu/record=b1253621~S1*cat
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