Extension of NXFEM to nonconforming finite elements

D. Capatina, H. El-Otmany, D. Graebling and R. Luce

Mathematics and Computers in Simulation (MATCOM), 2017, vol. 137, issue C, 226-245

Abstract: In this paper, we consider triangular nonconforming finite element approximations of an interface elliptic problem. We propose two extensions of the conforming Nitsche’s extended finite element method to the nonconforming case. The first one is obtained by adding stabilisation terms on the cut edges, and the second one by modifying the Crouzeix–Raviart basis functions on the cut cells. Both discrete problems are uniformly stable and yield optimal a priori error estimates, uniformly with respect to the diffusion parameters. Moreover, we show that they exhibit the same robustness with respect to the position of the interface as the classical conforming method. We then validate these results numerically. Finally, we propose a nonconforming approximation of the interface Stokes problem based on the modified Crouzeix–Raviart elements and we illustrate it numerically.

Keywords: Interface; NXFEM; Nonconforming finite elements; Robustness (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:137:y:2017:i:c:p:226-245

DOI: 10.1016/j.matcom.2016.12.009

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