TY - JOUR
T1 - Mixed Finite Volume Method for Elliptic Problems on Non-Matching Multi-Block Triangular Grids
AU - Yanni Gao, Junliang Lv & Lanhui Zhang
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 456
EP - 476
PY - 2017
DA - 2017/06
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10017.html
KW - Mixed finite volume method, error estimate, multi-block domain, non-matching grids.
AB - <p style="text-align: justify;">This article presents a mixed finite volume method for solving second-order elliptic
equations with Neumann boundary conditions. The computational domains can be decomposed
into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across
the sub-domain boundaries. We define a conforming triangular partition on each sub-domains
independently, and employ the standard mixed finite volume method within each sub-domain.
On the interfaces between different sun-domains, the grids are non-matching. The Robin type
boundary conditions are imposed on the non-matching interfaces to enhance the continuity of the
pressure and flux. Both the solvability and the first order rate of convergence for this numerical
scheme are rigorously proved. Numerical experiments are provided to illustrate the error behavior
of this scheme and confirm our theoretical results.</p>