GEOMETRIC PDES: THEORY, NUMERICS AND APPLICATIONS - RICARDO H. NOCHETTO - UNIVERSITY OF MARYLAND
The purpose of this course is to discuss elements of differential geometry in the context of analysis and approximation of geometric partial differential equations (PDEs). This includes the study of variations of functionals with respect to shape and applications to several geometric flows, finite element methods for the Laplace-Beltrami operator, nonlinear plate theory and liquid crystals. The emphasis is on variational formulations, approximation, and Gamma-convergence.
2. Elements of Differential Geometry
3. Shape Differential Calculus
4. Finite Element Methods for the Laplace-Beltrami Operator
5. Geometric Gradient Flows
7. Nonlinear Plate Theory
8. Director Fields and Liquid Crystals