Conducting Finite Element Convergence Studies Using COMSOL 4.0
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Date
2010
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Citation of Original Publication
Trott, David W. & Matthias K. Gobbert. “Conducting Finite Element Convergence Studies Using COMSOL 4.0.” In Proceedings of the COMSOL Conference 2010 Boston (2010). https://www.comsol.com/paper/conducting-finite-element-convergence-studies-using-comsol-4-0-8054.
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Abstract
In order to gauge how reasonable a finite element solution to a partial differential equation is on a given mesh, a common strategy is to
refine the mesh, compute the solution on the finer
mesh, and use the solutions on the two meshes for
a qualitative comparison. The theory of the finite element method (FEM) makes these comparisons quantitative by estimating the convergence
order of the FEM error on a sequence of progressively finer meshes. We will show how to carry out
convergence studies of this type in the graphical
user interface of COMSOL 4.0 on the example of
Lagrange elements of varying polynomial degrees,
which will also bring out the benefit of using higher
order elements.