FEM Convergence for PDEs with Point Sources in 2-D and 3-D
Links to Fileshttps://www.comsol.com/paper/fem-convergence-for-pdes-with-point-sources-in-2-d-and-3-d-26022
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Type of Work6 pages
Citation of Original PublicationGobbert, M., Kalayeh, K. M., Graf, J. S. FEM Convergence for PDEs with Point Sources in 2-D and 3-D. Presented at COMSOL Conference 2015, Boston, MA..
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Dirac delta distribution
mesh re finement
High Performance Computing Facility (HPCF)
Numerical theory provides the basis for quantification of 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 elliptic test problems in two and three space dimensions that demonstrate this theory by computing the convergence order of the FEM error. In particular, we 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 compared to problems with smooth right-hand sides and thus can be most efficiently solved by low-order FEM such as linear Lagrange elements.