We propose a class of weighted compact central schemes for solving hyperbolic conservation laws. The linear version can be considered as high-order extension the Lax–Friedrichs scheme and element solution scheme. On every cell, is approximated by Pth-order polynomial which all DOFs are stored updated separately. cell average classical finite volume constructed based on space-time staggered mesh...

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...

Central schemes may serve as universal finite-difference methods for solving nonlinear convection–diffusion equations in the sense that they are not tied to the specific eigenstructure of the problem, and hence can be implemented in a straightforward manner as black-box solvers for general conservation laws and related equations governing the spontaneous evolution of large gradient phenomena. T...

We present a discontinuous Galerkin method for melting/solidification problems based on the “linearized enthalpy approach,” which is derived from conservative form of energy transport equation and does not depend use so-called mushy zone. symmetric interior penalty Lax–Friedrichs flux to discretize diffusive convective terms, respectively. Time discretized with second-order implicit backward di...

The main aim of the current work is to apply Roe+Lax–Friedrichs (LF) hybrid entropy-stable scheme simulation three-dimensional ambient solar wind. governing equations for wind flow and magnetic field utilize entropy-consistent nine-wave divergence diminishing ideal magnetohydrodynamics (MHD) equations, which are symmetric Galilean invariant with some nonconservative terms proportional or gradie...

Liftings of endofunctors on sets to relations are commonly used capture bisimulation coalgebras. Lax versions have been in those cases where strict lifting fails bisimilarity, as well modeling other notions simulation. This paper provides tools for defining and manipulating lax liftings. As a central result, we define notion distributive law functor over the powerset monad, show that there is a...

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

We consider some natural connections which arise between right-flat (p, q) para-conformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a " Lax p-tuple " of linear differential operators, depending a spectral parameter which lives in (q − 1)-dimensional complex projective space. Generally, the differential operators contain partial derivatives ...