Disputas: Martin Werner Licht

Diplom Math. Martin Werner Licht ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.:

On the A Priori and A Posteriori Error Analysis in Finite Element Exterior Calculus

 

Martin Werner Licht

Tid og sted for prøveforelesning

15. juni 2017 kl. 10.15, Aud. 4 Vilhelm Bjerknes' hus

Bedømmelseskomité

  • Professor Ralf Hiptmair, Eidgenössische Technische Hochschule Zürich
  • Associate Professor Alan Demlow, Texas A&M University 
  • Professor Michael S. Floater, Universitetet i Oslo

Leder av disputas

Professor Hans Brodersen, Matematisk institutt, Universitet i Oslo

Veiledere

Sammendrag

The dissertation addresses the foundations of the finite element method within the framework of finite element exterior calculus. This includes the a priori error analysis and the a posteriori error analysis.

The scientific work addresses the reliability of numerical simulations. Specifically, the foundations of finite element methods are studied from the perspective of differential geometry. These abstract techniques have wide-ranging applications for the theoretical understanding of numerical simulations.

A special focus of the dissertation is the a priori error analysis, which estimates the accuracy of the numerical simulation prior to the actual computation in terms of discretization parameters. Commuting projection operators are an important component. We extend the known error analysis to weakly Lipschitz domains and discuss mixed boundary conditions.

Another major point of investigationis the a posteriori error analysis. Here, the accuracy of the simulation is estimated only after an approximation has been computed. We present an important advancement in the a posteriori error analysis of numerical electromagnetism. 

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Publisert 30. mai 2017 11:21 - Sist endret 13. juni 2017 10:36