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

Journal article

The non-linear Laplacian involves the differential equation -▽·(|▽u|α-2▽u) = f a.e. in Ω where α∈(1, ∞) and Ω 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.

Authors: Ainsworth, M; Kay, D

• Publication status: Published
• Publisher: Elsevier
• Journal: APPLIED NUMERICAL MATHEMATICS
• Volume: 34
• Issue: 4
• Pages: 329-344
• Publication date: 2000-08-01
• DOI: 10.1016/S0168-9274(99)00040-9
• ISSN: 0168-9274
• Language: English
• Keywords: p-Laplacian; a priori error estimation; hp-finite element method