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

The non-linear Laplacian involves the differential equation View the MathML source 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.