Si dà avviso che la prima lezione del corso tenuto dal prof. Ricardo H. Nochetto

Geometric Partial Differential Equations: Theory and Approximation

nell’ambito del progetto ‘Collegiale non residente’ dell’Università di Pavia

si terrà martedì 23/5 alle ore 16:15 presso il Collegio Nuovo.

Nella prima lezione verrà presentata una introduzione al Corso, e verranno fissati in accordo con gli studenti gli incontri successivi.

Qui sotto potete trovare un programma del corso:

————————– descrizione breve del corso ———————————-

Geometric Partial Differential Equations: Theory and Approximation

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.

———————————– programma del corso ————————————

Geometric Partial Differential Equations: Theory and Approximation

1. Introduction

Shape differential calculus: examples

2. Elements of Differential Geometry

Parametric surfaces: parametrizations, normal, area element
Tangential differential operators
Signed distance function
First and second fundamental forms
Divergence theorem on surfaces
The Laplace-Beltrami operator

3. Shape Differential Calculus

The velocity method
Material and shape derivatives
Shape derivatives of domain and contour integrals
Shape derivatives of geometric quantities
Shape derivatives of solutions of boundary value problems

4. Finite Element Methods for the Laplace-Beltrami Operator

Parametric FEM
Trace FEM
Narrow band FEM

Motivation: Allen-Cahn and Cahn-Hilliard models
Mean curvature flow
Optimal shape design
Surface diffusion
Willmore flow
Biomembranes: Helfrich flow

6. Gamma-Convergence

Definition
Convergence of absolute minimizers
Example: model reduction

7. Nonlinear Plate Theory

Nonlinear Kirchhoff model: large deformations and isometries
Bilayer plates
FEMs for bilayers
Gamma-convergence