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• W2084377449 abstract "Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves integrating their traces on the boundary of the domain, while the other evaluates integrals in the volume. Usually, the two BVPs can only be solved approximately, for instance, by finite element methods. However, when used with finite element solutions, the equivalence of the two formulas breaks down. By means of a comprehensive convergence analysis, we establish that the volume based expression for the shape gradient generally offers better accuracy in a finite element setting. The results are confirmed by several numerical experiments." @default.
• W2084377449 created "2016-06-24" @default.
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• W2084377449 date "2014-08-28" @default.
• W2084377449 modified "2023-10-18" @default.
• W2084377449 title "Comparison of approximate shape gradients" @default.
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• W2084377449 doi "https://doi.org/10.1007/s10543-014-0515-z" @default.
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