Analysis and Applied Mathematics Seminar
Sara Pollock
Texas A&M
Regularization and adaptivity in the approximation of quasilinear PDE
Abstract: I will introduce a class of nonlinear elliptic problems featuring solution-dependent and gradient-dependent diffusion. I will discuss some of the ways standard solution techniques can fail to resolve these nonlinear problems when they feature thin layers and steep gradients in their coefficients; and, I will introduce a framework that can be used to solve such problems starting from a coarse finite element discretization. The framework features a sequence of partial solves of regularized problems used to determine refinement of the mesh to resolve the problem coefficients and data. Adaptivity is used both for mesh refinement and automatic control of the regularization parameters to ultimately solve the discrete problem efficiently and without regularization. Numerical examples will illustrate the ideas and demonstrate the presented algorithm.
Monday April 25, 2016 at 4:00 PM in SEO 636