We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of th...

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...

Auxihary theorems allowing to extend the theory of curved finite éléments introduced m [2], [3] to the case ofboundary value problems with varions stable and unstable boundary conditions are proved As an example the problem of bending of thin elastic plates is considered Résumé — OM démontre des théorèmes auxiliaires qui permettent d'étendre la théorie des éléments finis courbes présentée dans ...

Using E1(M)-Dirac structures, a notion introduced by A. Wade, we obtain conditions under which a submanifold of a Jacobi manifold has an induced Jacobi structure, generalizing the result obtained by Courant for Dirac structures and submanifolds of a Poisson manifold.

GLOBAL ENTROPY SOLUTIONS IN L∞ TO THE EULER EQUATIONS AND EULER-POISSON EQUATIONS FOR ISOTHERMAL FLUIDS WITH SPHERICAL SYMMETRY ∗ GUI-QIANG CHEN† AND TIAN-HONG LI† Abstract. We prove the existence of global entropy solutions in L∞ to the multidimensional Euler equations and Euler-Poisson equations for compressible isothermal fluids with spherically symmetric initial data that allows vacuum and ...

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

A finite difference method is developed for solving symmetric positive differential equations in the sense of Friedrichs. The method is applicable to partial differential equations of mixed type with more general boundary conditions. The method is shown to have a convergence rate of 0(hxl2), h being the size of mesh grid. Some numerical results are presented for a model problem of forward-backw...