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Erschienen in:
A Mixed Finite Element Method for Modeling the Fluid Exchange Between Microcirculation and Tissue Interstitium Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Stabilized X-FEM for Heaviside and Nonlinear Enrichments

verfasst von : Giulio Ventura, Claudia Tesei

Erschienen in: Advances in Discretization Methods

Verlag: Springer International Publishing

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Abstract

One of the drawbacks of the eXtended Finite Element Method and similar approaches, like the Generalized Finite Element Method, is the problem of ill-conditioning of the related systems of equations at the solution stage. This occurs for example in Heaviside function enrichments when the discontinuity is close to discretisation nodes but also for non-linear enrichment functions used in conjunction to geometric enrichment domains. In the present work the motivation of ill-conditioning is analyzed to derive a novel methodology for stabilization, based on setting proper constraints for the variables. This methodology does not impact on the initial formulation nor in the element stiffness computation, so that it is very effective for engineering applications. Results are analyzed in 1D and 3D to show its performance and properties.

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Vorheriges Kapitel Adaptive Discontinuous Galerkin Methods on Polytopic Meshes
Nächstes Kapitel An Adaptive Fictitious Domain Method for Elliptic Problems
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Metadaten
Titel
Stabilized X-FEM for Heaviside and Nonlinear Enrichments
verfasst von
Giulio Ventura
Claudia Tesei
Copyright-Jahr
2016
Buch
Advances in Discretization Methods

Print ISBN: 978-3-319-41245-0

Electronic ISBN: 978-3-319-41246-7

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-41246-7_10

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