TY - JOUR
T1 - The Mixed Finite Volume Methods for Stokes Problem Based on MINI Element Pair
AU - Yang , Hongtao
AU - Li , Yonghai
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 134
EP - 151
PY - 2022
DA - 2022/11
SN - 20
DO - http://doi.org/ 10.4208/ijnam2023-1006
UR - https://global-sci.org/intro/article_detail/ijnam/21207.html
KW - Stokes problem, MINI element, mixed finite volume methods, inf-sup condition.
AB - <p style="text-align: justify;">In this paper, we present and analyze MINI Mixed finite volume element methods
(MINI-FVEM) for Stokes problem on triangular meshes. The trial spaces for velocity and pressure
are chosen as MINI element pair, and the test spaces for velocity and pressure are taken as the
piecewise constant function spaces on the respective dual grid. It is worth noting that the bilinear
form derived from the gradient operator and the bilinear form derived from the divergence are
unsymmetric. With the help of two new transformation operators, we establish the equivalence of
bilinear forms for gradient operator between finite volume methods and finite element methods,
and the equivalence of bilinear forms for divergence operator between finite volume methods and
finite element methods, so the inf-sup conditions are obtained. By the element analysis methods,
we give the positive definiteness of bilinear form for Laplacian operator. Based on the stability,
convergence analysis of schemes are established. Numerical experiments are presented to illustrate
the theoretical results.</p>