Volume 50, Number 5, September-October 2016
|Page(s)||1561 - 1583|
|Published online||20 September 2016|
Higher-order finite element methods for elliptic problems with interfaces∗
1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
2 Department of Mathematical Sciences at Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA
Received: 13 May 2015
Revised: 23 September 2015
Accepted: 24 November 2015
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.
Mathematics Subject Classification: 65N30 / 65N15
Key words: Interface problems / finite elements / pointwise estimates
An earlier version of this paper appeared on November 13, 2014 in http://www.brown.edu/research/projects/scientific-computing/reports/2014
© EDP Sciences, SMAI 2016
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