Approximation theory for the hp-version finite element method and application to the non-linear Laplacian

The non-linear Laplacian involves the differential equation -del . (\del u\(alpha-2) del u) = f a.e. in Omega where alpha is an element of (1, infinity) and Omega is a polygonal domain. The classical error estimates for the h version finite element approximation are generalized to the hp version, when applied to locally quasi-uniform meshes of quadrilateral elements. The estimates are expressed as an explicit function of the mesh-size h and the order p of the elements. The estimates include the case when the solution belongs to a Sobolev class and also when the solution has algebraic singularities due to the geometry of the domain. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.