TY - JOUR

T1 - Analysis of piecewise linear approximations to the generalized stokes problem in the velocity-stress-pressure formulation

AU - Yang, Suh Yuh

N1 - Funding Information:
This work was supported in part by the National Science Council of Taiwan, under grants NSC 89-2115-M-008-030 and NSC 90-2115-M-008-008.

PY - 2002/10/1

Y1 - 2002/10/1

N2 - In this paper we study continuous piecewise linear polynomial approximations to the generalized Stokes equations in the velocity-stress-pressure first-order system formulation by using a cell vertex finite volume/least-squares scheme. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the discretization process is accomplished. This combined approach has the advantages of both finite volume and least-squares approaches. An error estimate in the H1 product norm for continuous piecewise linear approximating functions is derived. It is shown that, with respect to the order of approximation for H2-regular exact solutions, the method exhibits an optimal rate of convergence in the H1 norm for all unknowns, velocity, stress, and pressure.

AB - In this paper we study continuous piecewise linear polynomial approximations to the generalized Stokes equations in the velocity-stress-pressure first-order system formulation by using a cell vertex finite volume/least-squares scheme. This method is composed of a direct cell vertex finite volume discretization step and an algebraic least-squares step, where the least-squares procedure is applied after the discretization process is accomplished. This combined approach has the advantages of both finite volume and least-squares approaches. An error estimate in the H1 product norm for continuous piecewise linear approximating functions is derived. It is shown that, with respect to the order of approximation for H2-regular exact solutions, the method exhibits an optimal rate of convergence in the H1 norm for all unknowns, velocity, stress, and pressure.

KW - Elasticity equations

KW - Finite volume methods

KW - Generalized stokes equations

KW - Least squares

KW - Velocity-stress-pressure formulation

UR - http://www.scopus.com/inward/record.url?scp=0036773076&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(02)00392-8

DO - 10.1016/S0377-0427(02)00392-8

M3 - 期刊論文

AN - SCOPUS:0036773076

VL - 147

SP - 53

EP - 73

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1

ER -