Extra seminar Computational Mathematics- Dr. G. Gantner University of Amsterdam

Title: Adaptive Isogeometric Finite Element Method

Abstract:

Isogeometric analysis (IGA) is a relatively new approach to numerically approximate the solution of partial differential equations (PDEs). For the approximation, the same functions are used that are used to represent the considered domain in Computer Aided Design (CAD). Usually, CAD is based on the tensor product of univariate splines. The latter are piecewise polynomials with certain differentiability properties. In order to optimally resolve any singularities of the PDE solution, local refinement of the underlying mesh is required. Since this is essentially not possible for standard tensor product splines, several extensions have been developed, e.g., hierarchical splines, T-splines or LR-splines.

In this talk, we consider adaptive isogeometric finite element methods (FEMs), which generate a sequence of locally refined meshes and corresponding discrete solutions. Here, the local refinement is governed by a suitable a posteriori computable error estimator. We show convergence of the estimator with optimal algebraic rate with respect to the degrees of freedom.