What is it about?
In engineering computations, curved domains have to be replaced in the finite element method by polygons. This gives rise to the mathematical question: What is the relation between the original problem and the numerical problem? In this contribution we positively answer the question.
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Why is it important?
The worth of numerical computations is strongly increased by a mathematical justification!
Perspectives
In this contribution we have focused our attention on convex domains that are replaced by convex polygons. In many engineering applications nonconvex domains are used. To our best knowledge, the corresponding analysis remains to be done.
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains, Applicable Analysis, October 2013, Taylor & Francis,
DOI: 10.1080/00036811.2012.724404.
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