Finite Element Convergence for Time-Dependent PDEs with a Point Source in COMSOL 4.2

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TrottGobbertCOMSOL2011.pdf (2.06 MB)

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https://userpages.umbc.edu/~gobbert/papers/TrottGobbertCOMSOL2011.pdf

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http://hdl.handle.net/11603/11666

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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2011

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conference paper pre-print
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Subjects

Heat equation
a priori error estimate
convergence study
mesh refinement
UMBC High Performance Computing Facility (HPCF)

Abstract

The FEM theory provides the basis for quantification on the accuracy and reliability of a numerical solution by the a priori error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents information on the techniques needed in COMSOL 4.2 to enable computational studies that demonstrate this theory for time-dependent problems, in extension of previous work on stationary problems. These techniques can be used in many general settings, including when the analytic PDE solution is not known.