TY - JOUR
T1 - Linear and Quadratic Finite Volume Methods on Triangular Meshes for Elliptic Equations with Singular Solutions
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 244
EP - 264
PY - 2016
DA - 2016/03
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/437.html
KW - Finite volume method, singular solution, optimal convergence rate.
AB - <p style="text-align: justify;">This paper is devoted to the presentation and analysis of some linear and quadratic
finite volume (FV) schemes for elliptic problems with singular solutions due to the non-smoothness
of the domain. Our FV schemes are constructed over specially-designed graded triangular meshes.
We provide sharp parameter selection criteria for the graded mesh, such that both the linear and
quadratic FV schemes achieve the optimal convergence rate approximating singular solutions in $H^1$. In addition, we show that on the same mesh, a linear FV scheme obtains the optimal rate of
convergence in $L^2$. Numerical tests are provided to verify the analysis.</p>