TY - JOUR
T1 - Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 505
EP - 519
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/781.html
KW - Transient Stokes equations, stabilized finite volume method, inf-sup condition, local Gauss integrals, optimal error estimate, stability.
AB - <p style="text-align: justify;">This paper is concerned with the development and study of a stabilized finite volume
method for the transient Stokes problem in two and three dimensions. The stabilization is based on two local Gauss integrals and is parameter-free. The analysis is based on a relationship between this new finite volume method and a stabilized finite element method using the lowest equal-order
pair (i.e., the $P_1$-$P_1$ pair). An error estimate of optimal order in the $H^1$-norm for velocity and
an estimate in the $L^2$-norm for pressure are obtained. An optimal error estimate in the $L^2$-norm
for the velocity is derived under an additional assumption on the body force.</p>