Die Urkunden Friedrichs II., Teil 3: 1218–1220, bearb. von Walter Koch unter Mitwirkung Klaus Höflinger, Joachim Spiegel und Christian Friedl (MGH der deutschen Könige Kaiser 14,3), Hannover: Monumenta Germaniae Historica 2010. XCII, 870 S. sowie 32 Abb. ISBN 978-3-7752-2003-3. Ln. € 150,–

We study time step restrictions due to linear stability constraints of Runge-Kutta Discontinuous Galerkin methods on triangular grids. The scalar advection equation is discretized in space by the Discontinuous Galerkin method with either the Lax-Friedrichs flux or the upwind flux, and integrated in time with various Runge-Kutta schemes designed for linear wave propagation problems or non-linear...

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of a continuous function in one dimension higher, we can treat the corresponding level set equation using the...

We establish some fundamental relations between Dirac subbundles L for the generalized Courant algebroid (A⊕A, φ+W ) over a differentiable manifold M and the associated Dirac subbubndles L̃ for the corresponding Courant algebroid Ã⊕ Ã over M × IR.

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...

Abstract. In dimension 2, the Horgan-Payne angle serves to construct a lower bound for the inf-sup constant of the divergence arising in the so-called LBB condition. This lower bound is equivalent to an upper bound for the Friedrichs constant. Explicit upper bounds for the latter constant can be found using a polar parametrization of the boundary. Revisiting carefully the original paper which e...

We consider the question: To what extend does the Weyl function (i.e., the abstract Dirichlet-to-Neumann map) see the same singularities as the resolvent of some restriction of the maximal operator. The proper, so-called detectable, subspace will be introduced and analyzed for particular examples, such as, Schrodinger operators, Hain–Lust operators, and (if time permits), the Friedrichs model o...

In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the fermions with the discrete and continuous sectors of the bosonic degrees of freedom leads to a system of coupled equations, whose solutions are found by appl...

Abstract. We prove a compact embedding theorem in a class of spaces of piecewise H functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the Rellich–Kondrachov theorem. It is used to prove generalizations to piecewise functions of nonstandard Poincaré–Friedrichs inequalities. It can be used to prove Ko...

An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of piecewise deterministic Markov processes [9], including a broader category of random systems. The corresponding Liouville-Master Equation is established and the upwind method is applied to numerical calculation of the distribution function. The convergence of the numerical solutio...