We extend our recent work with K. Zumbrun on long-time stability of multidimensional noncharacteristic viscous boundary layers of a class of symmetrizable hyperbolicparabolic systems. Our main improvements are (i) to establish the stability for a larger class of systems in dimensions d ≥ 2, yielding the result for certain magnetohydrodynamics (MHD) layers; (ii) to drop a technical assumption on...

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein’s equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift...

We consider the solution of ill-conditioned symmetric and positive definite large sparse linear systems of equations. These arise, for instance, when using some symmetrizable preconditioning technique for solving a general (possibly unsymmetric) ill-conditioned linear system, or in domain decomposition of a numerically difficult elliptic problem. We are also concerned with the consecutive solut...

We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree p and p +...

We described in [7] a monoid b G acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid with unit group a Kac-Moody group G. Now we find natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the monoid b G on Ω. These extensions are partly motivated by represen...

We give a formula for the universal R-matrix of the quantized universal enveloping algebra Uq(g). This is similar to a previous formula due to Kirillov-Reshetikhin and Levendorskii-Soibelman, except that where they use the action of the braid group element Tw0 on each representation V , we show that one can instead use a system of weight preserving endomorphisms. One advantage of our constructi...

Kirillov-Reshetikhin and Levendorskii-Soibelman developed a formula for the universal R-matrix of Uq(g) of the form R = (X ⊗X)∆(X). The action of X on a representation V permutes weight spaces according to the longest element in the Weyl group, so is only defined when g is of finite type. We give a similar formula which is valid for any symmetrizable KacMoody algebra. This is done by replacing ...

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based...

We give the definition of a kind of building I for a symmetrizable KacMoody group over a field K endowed with a dicrete valuation and with a residue field containing C. Due to some bad properties, we call this I a hovel. Nevertheless I has some good properties, for example the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semi-simpl...