Variational Convergence and Discrete Minimal Surfaces

by Henrik Schumacher
Doctoral thesis
Date of Examination:2014-12-09
Date of issue:2015-11-05
Advisor:Prof. Dr. Max Wardetzky
Referee:Prof. Dr. Max Wardetzky
Referee:Prof. Dr. Russell Luke
Referee:Prof. Dr. Samir Adly
Persistent Address: http://dx.doi.org/10.53846/goediss-5334

 

 

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Abstract

English

This work is concerned with the convergence behavior of the solutions to parametric variational problems. An emphasis is put on sequences of variational problems that arise as discretizations of either infinite-dimensional optimization problems or infinite-dimensional operator problems. Finally, the results are applied to discretizations of the Douglas-Plateau problem and of a boundary value problem in nonlinear elasticity.
Keywords: Hencky elasticity; Ritz-Galerkin method; finite element method; minimal surfaces; Douglas-Plateau problem
 
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