QUASI-NORM TECHNIQUES FOR FINITE ELEMENT APPROXIMATION OF p-LAPLAICAN
نویسنده
چکیده
The p-Laplacian problem is one of the typical examples of degenerate nonlinear systems arising from nonlinear diffusion and filtration, powerlaw materials and quasi-Newtonian flows. In this article we give a survey of quasi-norm techniques to establish optimal error estimates for finite element approximation of p-Laplacian.
منابع مشابه
Finite element quasi-interpolation and best approximation
This paper introduces a quasi-interpolation operator for scalarand vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces W r,p, where p ∈ [1,∞] and the smoothness index r can be arbitraril...
متن کاملA posteriori FE error control for p-Laplacian by gradient recovery in quasi-norm
A posteriori error estimators based on quasi-norm gradient recovery are established for the finite element approximation of the p-Laplacian on unstructured meshes. The new a posteriori error estimators provide both upper and lower bounds in the quasi-norm for the discretization error. The main tools for the proofs of reliability are approximation error estimates for a local approximation operat...
متن کاملDiscontinuous Galerkin Finite Element Approximation of Quasilinear Elliptic Boundary Value Problems Ii: Strongly Monotone Quasi-newtonian Flows
In this article we develop both the a priori and a posteriori error analysis of hp– version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local ...
متن کاملFuzzy Best Simultaneous Approximation of a Finite Numbers of Functions
Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کامل