Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method

This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on regularization and a scaling in time and space, the problem is discretized implicitly in time by the backward Euler scheme and discretized in space by C⁰ Interior Penalty Discontinuous Galerkin (C⁰IPDG) method. In particular, it is showed that at each time instant the C⁰IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower semi-continuous objective functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C⁰IPDG-norm and the L²-norm. A documentation of numerical results is provided illustrating the performance of the C⁰IPDG method and predictor corrector continuation strategies.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2018

Author dc:creator

• Bhandari, Chandi Prasad 1985-

Advisor dc:contributor.advisor

• Hoppe, Ronald W.

Committee members dc:contributor.committeemember

• Pan, Tsorng-Whay
• Sanders, Richard
• Sharma, Natasha S.

• Surface relaxation
• Galerkin approximation
• C 0 Interior Penalty
• Discontinuous Galerkin Approximation
• Mixed finite element methods

Statement dc:rights

• The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/10657/3434

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/3434