A priori error estimates of the DtN-FEM: fluid-solid interaction problems

Tao Yin, Liwei Xu

Published 2016-09-02Version 1

We consider the finite element method solving a fluid-solid interaction (FSI) problem in two dimensions. The original problem is reduced to an equivalent nonlocal boundary value problem through an exact Dirichlet-to-Neumann (DtN) mapping defined on an artificial boundary enclosing the solid. The solvability results are established for the corresponding variational problem and its modified form resulting from truncation of the DtN mapping. Regarding to the numerical solutions, we derive a priori error estimates involving the effects of both finite element discretization and infinite series truncation. Numerical examples are presented to illustrate the accuracy of numerical schemes and validate the theoretical results.