TY - JOUR
T1 - Robust and Efficient Mixed Hybrid Discontinuous Finite Element Methods for Elliptic Interface Problems
AU - Zhu , Jiang
AU - Vargas Poblete , Héctor Andrés
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 767
EP - 788
PY - 2019
DA - 2019/08
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13253.html
KW - Elliptic interface problems, discontinuous Galerkin finite element methods, mixed and hybrid methods, Nitsche’s penalty method, sensitivities of interface location and material heterogeneities.
AB - <p style="text-align: justify;">Because of the discontinuity of the interface problems, it is natural to apply the
discontinuous Galerkin (DG) finite element methods to solve those problems. In this work, both
fitted and unfitted mixed hybrid discontinuous Galerkin (MHDG) finite element methods are
proposed to solve the elliptic interface problems. For the fitted case, the problems can be solved
directly by MHDG method. For the unfitted case, the broken basis functions (unnecessary to
satisfy the jump conditions) are introduced to those elements which are cut across by interface,
the weights depending on the volume fractions of cut elements and the different diffusions (or
material heterogeneities) are used to stabilize the method, and the idea of the Nitsche&#39;s penalty
method is applied to guarantee the jumps on the interface parts of cut elements. Unlike the
immersed interface finite element methods (IIFEM), the two jump conditions are enforced weakly
in our variational formulations. So, our unfitted interface MHDG method can be applied more
easily than IIFEM to general cases, particularly when the immersed basis function cannot be
constructed. Numerical results on convergence and sensitivities of both interface location within a
cut element and material heterogeneities show that the proposed methods are robust and efficient
for interface problems.</p>