We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.

1. Harmonic analysis on H 2. Meromorphic continuation up to the critical line 3. Sobolev inequality/imbedding 4. Eventually-vanishing constant terms 5. Compactness of Sob(Γ\H)a → L(Γ\H) 6. Discreteness of cuspforms 7. Meromorphic continuation beyond the critical line 8. Discrete decomposition of truncated Eisenstein series 9. Appendix: Friedrichs extensions 10. Appendix: simplest Maass-Selberg ...

In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell’s system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theo...

We discuss numerical stabilisation of dynamics governed by nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove exponential decay of the discrete solution to first– order finite volume schemes in conservative form. Decay rates are established for a large class of finite volume schemes including the Lax–Friedrichs scheme. Theore...

The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type scheme and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.

Submit Manuscript | http://medcraveonline.com Abbreviations: 1D: One-Dimensional; 2D: Two-Dimensional; 3D: Three-Dimensional; DGTD: Discontinuous Galerkin TimeDomain; FEs: Finite Elements; TM: Transverse Magnetic; TE: Transverse Electric; ODE: Ordinary Differential Equations; LSERK: Low-Storage Explicit Runge-Kutta; CFL: Courant-Friedrichs-Levy; TD: Time-Domain; PEC: Perfect Electric Conductor;...

Submit Manuscript | http://medcraveonline.com Abbreviations: 1D: One-Dimensional; 2D: Two-Dimensional; 3D: Three-Dimensional; DGTD: Discontinuous Galerkin TimeDomain; FEs: Finite Elements; TM: Transverse Magnetic; TE: Transverse Electric; ODE: Ordinary Differential Equations; LSERK: Low-Storage Explicit Runge-Kutta; CFL: Courant-Friedrichs-Levy; TD: Time-Domain; PEC: Perfect Electric Conductor;...

We study the existence of global-in-time weak solutions to a coupled microscopic-macroscopic bead-spring model which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ R, d = 2 or 3, for the velocity and the pressure of the fluid, with an ela...