Hilbert

Published configurations

Hilbert-space formulations and regularization.

\[ \alpha^2 \int_\Omega \nabla u : \nabla v \, dx + \int_\Omega u \cdot v \, dx = \ell(v) \]

H1a solves a regularized extension problem that converts a linear functional into a smooth field over the mesh. It is commonly used to extend boundary shape derivatives into volume descent directions, with a configurable length scale controlling smoothing and boundary conditions constraining the extension.

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