Constructive L2 Error Estimates for Finite Element Solutions of the Stokes Equations

Constructive L2 error estimates for finite element solutions of the Stokes equations are described. We show that the L2 error bounds for the velocity can be obtained in a posteriori and explicit a priori sense. Some numerical examples which confirm us the expected rates of convergence are presented.

[1]  M. Nakao.  Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration , 1993 .

[2]  Vivette Girault,et al.  Finite element approximation of the Navier-Stockes equations , 1979 .

[3]  Randolph E. Bank,et al.  A posteriori error estimates for the Stokes problem , 1991 .

[4]  I. Babuska,et al.  A‐posteriori error estimates for the finite element method , 1978 .

[5]  Roland Glowinski,et al.  An introduction to the mathematical theory of finite elements , 1976 .

[6]  Seiji Kimura,et al.  On the Best Constant in the Error Bound for theH10-Projection into Piecewise Polynomial Spaces , 1998 .

[7]  Nobito Yamamoto,et al.  Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains , 1993 .

[8]  Friedrich Goerisch,et al.  The Determination of Guaranteed Bounds to Eigenvalues with the Use of Variational Methods I , 1990, Computer Arithmetic and Self-Validating Numerical Methods.

[9]  Nobito Yamamoto,et al.  A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations , 1998 .

[10]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[11]  Cornelius O. Horgan,et al.  On inequalities of Korn, Friedrichs and Babuška-Aziz , 1983 .

[12]  Rüdiger Verfürth,et al.  A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[13]  M. Nakao,et al.  Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element , 1995 .

[14]  渡部 善隆.  Guaranteed Error Bounds for Finite Element Solutions of the Stokes Equations , 1996 .