An interface/boundary-unfitted eXtended HDG method for linear elasticity problems

Yihui Han, Xiao-Ping Wang, Xiaoping Xie

Published 2020-04-14Version 1

An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The method uses piecewise polynomials of degrees $k\ (>= 1)$ and $k-1$ respectively for the displacement and stress approximations in the interior of elements inside the subdomains separated by the interface, and piecewise polynomials of degree $k$ for the numerical traces of the displacement on the inter-element boundaries inside the subdomains and on the interface/boundary of the domain. Optimal error estimates in $L^2$-norm for the stress and displacement are derived, which are uniform with respect to the Lam\'e constant $\lambda$. Finally, numerical experiments confirm the theoretical results and show that the method also applies to the case of crack-tip domain.