A hk mortar spectral element method for the p-Laplacian equation

We present a constrained-vertex variant of the mortar spectral element method to solve the p-Laplacian equation. To show reliability of the method, first we investigate convergence rate of h-version and k-version for a sufficiently smooth solution. Then for solutions with limited regularity, we use a hk-strategy in which the size of elements is geometrically reduced towards the singularity while the polynomial degree is linearly reduced. In fact, we numerically study convergence rate of the hk mortar spectral element method in the L2-norm and H1-norm using geometrical meshes with elements of non-uniform polynomial degree. In this regard, we consider several benchmarks with various choices of the parameter p as well as geometric grading factors. To deal with possible degeneracy in the p-Laplacian operator, we add artificial diffusion to the original equation and then study the effects of this extra diffusion on convergence rate. To find the solution of highly nonlinear system arising from discretization we use an optimization technique based on the trust region method in which an analytical Jacobian matrix is utilized.