论文信息 - Besov regularity and new error estimates for finite volume approximations of the p-laplacian

Besov regularity and new error estimates for finite volume approximations of the p-laplacian

Summary.In [1], we have constructed a family of finite volume schemes on rectangular meshes for the p-laplacian and we proved error estimates in case the exact solution lies in W2,p. Actually, W2,p is not a natural space for solutions of the p-laplacian in the case p>2. Indeed, for general Lp’ data it can be shown that the solution only belongs to the Besov space In this paper, we prove Besov kind a priori estimates on the approximate solution for any data in Lp’. We then obtain new error estimates for such solutions in the case of uniform meshes

[1] F. Boyer,et al. Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes , 2007 .

[2] H. Triebel. Interpolation Theory, Function Spaces, Differential Operators , 1978 .

[3] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[4] John W. Barrett,et al. A further remark on the regularity of the solutions of the p -Laplacian and its applications to their finite element approximations , 1993 .

[5] Winfried Sickel,et al. Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations , 1996, de Gruyter series in nonlinear analysis and applications.

[6] Michael Gutnic,et al. Convergence of Finite Volume Approximations for a Nonlinear Elliptic-Parabolic Problem: A "Continuous" Approach , 2004, SIAM J. Numer. Anal..

[7] Jacques Simon,et al. Régularité de la solution d'un problème aux limites non linéaires , 1981 .

[8] John W. Barrett,et al. Finite element approximation of the p-Laplacian , 1993 .

[9] R. Glowinski,et al. Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[10] Franck Boyer,et al. Finite volume schemes for the p-Laplacian on Cartesian meshes , 2004 .

[11] S. Chow. Finite element error estimates for non-linear elliptic equations of monotone type , 1989 .