Solving the p-Laplace problem using Isogeometric Analysis

Stefan Tyoler

Jan. 26, 2021, 3:30 p.m. ZOOM

In this presentation the p-Laplace problem will be discussed. The p-Laplace problemis a nonlinear elliptic partial differential equation, that can show singular behaviour for specific choices of its characteristic parameter $p$. First the possible singular behaviour will be treated by looking at a perturbed problem that acts as a regularizationof these singularities. This nonlinear problem will be solved by the Picard method by iteratively solving linearized versions of the equation with Isogeometric methods (B-Spline basis). Thedifferential equation has Dirichletboundary conditions, where we consider elimination and Nitsche methods for their enforcement. Thenumerical experimentation with different examples will be presented and some known convergence rates will be confirmed.