Characterization of partial derivatives with respect to material parameters in a fluid-solid interaction problem (Q1650497)

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.