Convergence Order Studies for Elliptic Test Problems with COMSOL Multiphysics
| dc.contributor.author | Yang, Shiming | |
| dc.contributor.author | Gobbert, Matthias K. | |
| dc.date.accessioned | 2018-10-23T16:24:20Z | |
| dc.date.available | 2018-10-23T16:24:20Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | The convergence order of fi nite elements is related to the polynomial order of the basis functions used on each element, with higher order polynomials yielding better convergence orders. However, two issues can prevent this convergence order from being achieved: the poor approximation of curved boundaries by polygonal meshes and lack of regularity of the PDE solution. We show studies for Lagrange elements of degrees 1 through 5 applied to the classical test problem of the Poisson equation with Dirichlet boundary condition. We consider this problem in 1, 2, and 3 spatial dimensions and on domains with polygonal and with curved boundaries. The observed convergence orders in the norm of the error between FEM and PDE solution demonstrate that they are limited by the regularity of the solution and are degraded signifi cantly on domains with non-polygonal boundaries. All numerical tests are carried out with COMSOL Multiphysics. | en_US |
| dc.description.uri | https://userpages.umbc.edu/~gobbert/papers/YangGobbertTR2008COMSOL.pdf | en_US |
| dc.format.extent | 20 pages | en_US |
| dc.genre | technical report | en_US |
| dc.identifier | doi:10.13016/M2DN4005V | |
| dc.identifier.uri | http://hdl.handle.net/11603/11659 | |
| dc.language.iso | en_US | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.relation.ispartofseries | HPCF Technical Report;HPCF-2008-4 | |
| 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 | a priori error estimate | 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 | Convergence Order Studies for Elliptic Test Problems with COMSOL Multiphysics | en_US |
| dc.type | Text | en_US |