Numerische Mathematik Interpolation operators in Orlicz – Sobolev spaces

We study classical interpolation operators for finite elements, like the Scott–Zhang operator, in the context of Orlicz–Sobolev spaces. Furthermore, we show estimates for these operators with respect to quasi-norms which appear in the study of systems of p-Laplace type.

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

[2]  Ridgway Scott,et al.  Constructive polynomial approximation in Sobolev spaces , 1978 .

[3]  W. B. Liu,et al.  Quasi-Norm interpolation error estimates for the piecewise linear finite element approximation of p-Laplacian problems , 2005, Numerische Mathematik.

[4]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[5]  P. Clément.  Approximation by finite element functions using local regularization , 1975 .

[6]  B. Dacorogna.  Direct methods in the calculus of variations , 1989 .

[7]  Wenbin Liu,et al.  On Quasi-Norm Interpolation Error Estimation And A Posteriori Error Estimates for p-Laplacian , 2002, SIAM J. Numer. Anal..

[8]  Carsten Ebmeyer,et al.  Global Regularity in Fractional Order Sobolev Spaces for the p-Laplace Equation on Polyhedral Domains , 2005 .

[9]  W. B. Liu,et al.  Quasi-norm Error Bounds for the Nite Element Approximation of a Non-newtonian Ow , 1994 .

[10]  Lars Diening,et al.  Fractional estimates for non-differentiable elliptic systems with general growth , 2008 .

[11]  L. R. Scott,et al.  Finite element interpolation of nonsmooth functions satisfying boundary conditions , 1990 .

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

[13]  John W. Barrett,et al.  Finite-Element Approximation of Degenerate Quasi-Linear Elliptic and Parabolic Problems , 1994 .

[14]  C. Ebmeyer,et al.  Global regularity in Nikolskij spaces for elliptic equations with p-structure on polyhedral domains , 2005 .

[15]  Wenbin Liu,et al.  Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian , 2001, Numerische Mathematik.

[16]  F. Smithies,et al.  Convex Functions and Orlicz Spaces , 1962, The Mathematical Gazette.

[17]  M. Rao,et al.  Theory of Orlicz spaces , 1991 .