Solving the p-Laplace problem using Isogeometric Analysis
Stefan TyolerJune 1, 2021, 1:30 p.m. ZOOM
The stationary $p$-Laplace problem is a quasilinear elliptic partial differential equation,which arises (in simplified form) from modelling physical phenomena like the simulation of fluids in porous media or of non-newtonian fluids. The problem shows singular behaviour for specific choices of its characteristic parameter $p$. First, a perturbed problem that acts as a regularization of these singularities will be discussed. A short overview on existence and uniqueness will be presented by theoretical results about monotone operators.
Furthermore the variational formulation will be discretized by means of isogeometric methods (B-splines). The resulting nonlinear system of equations will be solved by the Picard iterative method. The differential equation has Dirichlet boundary conditions, where we consider strong and weak imposition of the Dirichlet data. The numerical experimentation with different examples will be presented and some known convergence rates will be confirmed.