TY - JOUR
T1 - The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 368
EP - 382
PY - 2016
DA - 2016/05
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/444.html
KW - Elliptic interface problem, non-homogeneous jump conditions, immersed finite volume element.
AB - <p style="text-align: justify;">In this paper, an immersed finite volume element (IFVE) method is developed for
solving some interface problems with nonhomogeneous jump conditions. Using the source removal
technique of nonhomogeneous jump conditions, the new IFVE method is the finite volume element
method applied to the equivalent interface problems with homogeneous jump conditions and have
properties of the usual finite volume element method. The resulting IFVE scheme is simple and
second order accurate with a uniform rectangular partition and the dual meshes. Error analyses
show that the new IFVE method with usual $O(h^2)$ convergence in the $L^2$ norm and $O(h)$ in
the $H^1$ norm. Numerical examples are also presented to demonstrate the efficiency of the new
method.</p>