FEM Convergence Studies for 2-D and 3-D Elliptic PDEs with Smooth and Non-Smooth Source Terms in COMSOL 5.1
| dc.contributor.author | Kalayeh, Kourosh M. | |
| dc.contributor.author | Graf, Jonathan S. | |
| dc.contributor.author | Gobbert, Matthias K. | |
| dc.date.accessioned | 2018-10-01T14:08:49Z | |
| dc.date.available | 2018-10-01T14:08:49Z | |
| dc.date.issued | 2015 | |
| dc.description.abstract | Numerical theory provides the basis for quanti cation on the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in COMSOL 5.1 to perform computational studies for an elliptic test problem in two and three space dimensions that demonstrate this theory by computing the convergence order of the FEM error. For a PDE with smooth right-hand side, linear Lagrange nite elements exhibit second order convergence for all space dimensions. We also show how to perform these techniques for a problem involving a point source modeled by a Dirac delta distribution as forcing term. This demonstrates that PDE problems with a non-smooth source term necessarily have degraded convergence order and thus can be most e ciently solved by low-order FEM such as linear Lagrange elements. Detailed instructions for obtaining the results are included in an appendix. | en_US |
| dc.description.sponsorship | The hardware used in the computational studies is part of the UMBC High Performance Computing Facility (HPCF). The facility is supported by the U.S. National Science Foundation through the MRI program (grant nos. CNS{0821258 and CNS{1228778) and the SCREMS program (grant no. DMS{0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See hpcf.umbc.edu for more information on HPCF and the projects using its resources. Co-author Graf acknowledges financial support as HPCF RA. | en_US |
| dc.description.uri | https://userpages.umbc.edu/~gobbert/papers/COMSOL51_HPCF2015.pdf | en_US |
| dc.format.extent | 10 pages | en_US |
| dc.genre | techical report | en_US |
| dc.identifier | doi:10.13016/M2X63B87B | |
| dc.identifier.uri | http://hdl.handle.net/11603/11427 | |
| dc.language.iso | en_US | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mechanical Engineering Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.relation.ispartof | UMBC Mathematics and Statistics Department | |
| dc.relation.ispartofseries | HPCF Technical Report;HPCF-2015-19 | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | |
| dc.subject | Poisson equation | en_US |
| dc.subject | point source | en_US |
| dc.subject | Dirac delta distribution | en_US |
| dc.subject | convergence study | en_US |
| dc.subject | mesh refinement | en_US |
| dc.subject | UMBC High Performance Computing Facility (HPCF) | en_US |
| dc.title | FEM Convergence Studies for 2-D and 3-D Elliptic PDEs with Smooth and Non-Smooth Source Terms in COMSOL 5.1 | en_US |
| dc.type | Text | en_US |