Issue |
ESAIM: M2AN
Volume 50, Number 5, September-October 2016
|
|
---|---|---|
Page(s) | 1561 - 1583 | |
DOI | https://doi.org/10.1051/m2an/2015093 | |
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
johnnyguzman@brown.edu
2 Department of Mathematical Sciences at Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA
msarkis@wpi.edu
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.