On time integration in the XFEM

By Thomas-Peter Fries, Andreas Zilian. 2009

87 citations recorded by the source corpus.

The extended finite element method (XFEM) is often used in applications that involve moving interfaces. Examples are the propagation of cracks or the movement of interfaces in two‐phase problems. This work focuses on time integration in the XFEM. The performance of the discontinuous Galerkin method in time (space–time finite elements (FEs)) and time‐stepping schemes are analyzed by convergence studies for different model problems. It is shown that space–time FE achieve optimal convergence rates. Special care is required for time stepping in the XFEM due to the time dependence of the enrichment functions. In each time step, the enrichment functions have to be evaluated at different time levels. This has important consequences in the quadrature used for the integration of the weak form. A time‐stepping scheme that leads to optimal or only slightly sub‐optimal convergence rates is systematically constructed in this work. Copyright © 2009 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/660b2b0854595b0056135fad3991348e0dd5d758

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “In Fries and Zilian [81], several one-step time-stepping schemes are analyzed for moving weak discontinuities.”
Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture (2014, unknown): “2009) and time stepping algorithms (Remmers et al. 2008; Fries and Zilian 2009).”
Higher‐order XFEM for curved strong and weak discontinuities (2009, methodology): “A similar test case has been presented by Fries and Zilian [46], who considered a rectilinear discontinuity in the space–time domain.”