2 research outputs found
An interface/boundary-unfitted eXtended HDG method for linear elasticity problems
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 and
respectively for the displacement and stress approximations in the interior of
elements inside the subdomains separated by the interface, and piecewise
polynomials of degree 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 -norm for the stress and
displacement are derived. Finally, numerical experiments confirm the
theoretical results and show that the method also applies to the case of
crack-tip domain.Comment: 21 pages, 14 figures. arXiv admin note: text overlap with
arXiv:1910.0976
An eXtended HDG method for Darcy-Stokes-Brinkman interface problems
This paper proposes an interface/boundary-unfitted eXtended hybridizable
discontinuous Galerkin (X-HDG) method for Darcy-Stokes-Brinkman interface
problems in two and three dimensions. The method uses piecewise linear
polynomials for the velocity approximation and piecewise constants for both the
velocity gradient and pressure approximations in the interior of elements
inside the subdomains separated by the interface, uses piecewise constants for
the numerical traces of velocity on the inter-element boundaries inside the
subdomains, and uses piecewise constants or linear polynomials for the
numerical traces of velocity on the interface. Optimal error estimates are
derived for the interface-unfitted X-HDG scheme. Numerical experiments are
provided to verify the theoretical results and the robustness of the proposed
method.Comment: 22 pages, 31 figure