Discontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions Max Jensen Doctor of Philosophy Corpus Christi College Michaelmas Term 2004 This work is concerned with the numerical solution of Friedrichs systems by discontinuous Galerkin finite element methods (DGFEMs). Friedrichs systems are boundary value problems with symmetric, positive, linear first-order partial differenti...

This paper is the third and last part of a work attempting to give a unified analysis of Discontinuous Galerkin methods. The purpose of this paper is to extend the framework that has been developed in part II for two-field Friedrichs’ systems associated with second-order PDE’s. We now consider two-field Friedrichs’ systems with partial L2-coercivity and three-field Friedrichs’ systems with an e...

Some notes on the Friedrichs Extension Theorem, for MATH 7130, Spring 2010.

6 Friedrichs, K. O., Mathematical Aspects of the Quantum Theory of Fields (New York: Interscience, 1953). 7Friedrichs, K. O., Lectures, Summer Conference on Mathematics and Modern Physical Theories, Boulder (1960). 8 Schwartz, J., Mass Renormalization and Spectral Shifts, N.Y.U. Research Report (1960). 9 Friedrichs, K. O., "Spectral theory of operators in Hilbert space," N.Y.U. lecture notes (1...

The systems of conservation laws have been used to model dynamical phase transitions in, for example, the propagating phase boundaries in solids and the van der Waals uid. When integrating such mixed hyperbolic-elliptic systems the Lax-Friedrichs scheme is known to give the correct solutions selected by a viscosity-capillarity criterion except a spike at the phase boundary which does not go awa...

Solutions of Friedrichs systems are in general not of Sobolev regularity and may possess discontinuities along the characteristics of the differential operator. We state a setting in which the well-posedness of Friedrichs systems on polyhedral domains is ensured, while still allowing changes in the inertial type of the boundary. In this framework the discontinuous Galerkin method converges in t...

^Let ii be a simply connected domain in C1 with the area measure dA . Let Pa be the orthogonal projection from L?(Q.,dA) onto the closed subspace of antiholomorphic functions in L2(Í2, dA). The Friedrichs operator Tçi associated to Í2 is the operator from the Bergman space L*(Q.) into L2(fi, dA) defined by Tnf = Paf. In this note, some smoothness conditions on the boundary of Í2 are given such ...