Characterization of partial derivatives with respect to material parameters in a fluid-solid interaction problem
For a fluid-solid interaction problem with Lipschitz interface, the authors investigate the partial Fréchet differentiability of the solutions and the approximate far-field-pattern with respect to solid material parameters. Differentiability is shown in the standard Sobolev framework, and the derivatives are characterized as solutions to inhomogeneous fluid-solid transmission problems. They also show that interior penalty discontinuous Galerkin method gives results with high precision and incurs almost no effect of discretization error accumulation.
sensitivity with respect to Lamé parameters
scientific article; zbMATH DE number 6898337
scientific article