Finalist EPFL doctorate Award 2009 - Stamm Benjamin
© 2009 EPFL
Benjamin Stamm's scientific work is (according to the opinion of the jury) ranking among the best 3 % PhD theses awarded by EPFL in 2008. Thesis EPFL, no 4135 (2008). Dir.: Alfio Quarteroni, Erik Burman.
Stabilization strategies for discontinuous Galerkin methods.
The subject of this thesis is the analysis of discontinuous Galerkin methods for linear partial differential equations of first or second order. Discontinuous Galerkin methods are known to satisfy a local mass conservation property. Taking a closer look one can observe that this property often depends on the method itself, i.e. on some method-dependent parameters. The main objective of this work is to design discontinuous Galerkin schemes satisfying a method-independent local mass conservation property still ensuring full stability and optimal convergence of the approximations.
Depending on the problem and the choice of the approximation space, the strategy to reach this goal might be different. We give a precise characterization of what type of stabilization term is needed in order to obtain a stable and optimally convergent numerical scheme.