A Nitsche finite element approach for elliptic problems with discontinuous Dirichlet boundary conditions

Baumann, Ramona; Wihler, Thomas (2018). A Nitsche finite element approach for elliptic problems with discontinuous Dirichlet boundary conditions. Computational methods in applied mathematics, 18(3), pp. 373-381. De Gruyter 10.1515/cmam-2017-0057

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We present a numerical approximation method for linear elliptic diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known singular functions as well as of an H²-regular part. The latter part is expressed in terms of an elliptic problem with regularized Dirichlet boundary conditions, and can be approximated by means of a Nitsche finite element approach. The discrete solution of the original problem is then defined by adding back the singular part of the exact solution to the Nitsche approximation. In this way, the discrete solution can be shown to converge of second order in the L²-norm with respect to the mesh size.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Baumann, Ramona and Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

1609-4840

Publisher:

De Gruyter

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

15 May 2019 18:16

Last Modified:

24 Oct 2019 20:49

Publisher DOI:

10.1515/cmam-2017-0057

ArXiv ID:

1707.00764v1

BORIS DOI:

10.7892/boris.125542

URI:

https://boris.unibe.ch/id/eprint/125542

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