Adaptive finite elements based on sensitivities for topological mesh changes
Adaptive finite elements based on sensitivities for topological mesh changes
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Start date: 16. March 2012
End date: 15. March 2018
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Abstract
We consider local refinements of finite element triangulations as continuous graph operations, for instance by splitting nodes and inflating edges to elements. This approach allows for the derivation of sensitivities for functionals depending on the finite element solution, which may in turn be used to define local refinement indicators. Thereby, we develop adaptive algorithms exploiting sensitivities for both hierarchical and non-hierarchical mesh changes, and analyze their properties and performance in comparison with established methods.