Superconvergence analysis of the MAC scheme for the two dimensional stokes problem

Lin, Yanping; Zou, Qingsong

doi:10.1002/num.22066

Cited by 3 publications

(1 citation statement)

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“…For research on the finite volume method whose velocity and pressure are both conforming elements space, they either use stablilized equal order pairs [22,21,32,36], or discrete continuity equations by finte element methods [22,32,10]. MAC-like(Marker-And-Cell) finite volume methods on staggered grids are studied in the papers [12,30,35]. As the same time, scholars also extended the finite volume method to the Navier-Stokes equations [25,23,24] and other complex fluid problems [34].…”

Section: Introductionmentioning

confidence: 99%

The Mixed Finite Volume Methods for Stokes Problem Based on MINI Element Pair

Li¹

2023

IJNAM

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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.

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