In this paper we further explore a local postprocessing technique, originally developed by Brambl... more In this paper we further explore a local postprocessing technique, originally developed by Bramble and Schatz [Math. Comp., 31 (1977), pp. 94--111] using continuous finite element methods for elliptic problems and later by Cockburn et al. [Math. Comp., 72 (2003), pp. 577--606] ...
The convergence to steady state solutions of the Euler equations for the fifth-order weighted ess... more The convergence to steady state solutions of the Euler equations for the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme with the Lax–Friedrichs flux splitting [7, (1996) J. Comput. Phys. 126, 202–228.] is studied through systematic numerical tests. Numerical evidence indicates that this type of WENO scheme suffers from slight post-shock oscillations. Even though these oscillations are small in magnitude
Advanced numerical approximation of nonlinear …, 1998
In these lecture notes we describe the constraction, analysis, and applica-tion of ENO (Essential... more In these lecture notes we describe the constraction, analysis, and applica-tion of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essen-tially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are ...
In this paper the authors review some recent work on high-order well-balanced schemes. A characte... more In this paper the authors review some recent work on high-order well-balanced schemes. A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Well-balanced schemes satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. They
In this paper we further explore a local postprocessing technique, originally developed by Brambl... more In this paper we further explore a local postprocessing technique, originally developed by Bramble and Schatz [Math. Comp., 31 (1977), pp. 94--111] using continuous finite element methods for elliptic problems and later by Cockburn et al. [Math. Comp., 72 (2003), pp. 577--606] ...
The convergence to steady state solutions of the Euler equations for the fifth-order weighted ess... more The convergence to steady state solutions of the Euler equations for the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme with the Lax–Friedrichs flux splitting [7, (1996) J. Comput. Phys. 126, 202–228.] is studied through systematic numerical tests. Numerical evidence indicates that this type of WENO scheme suffers from slight post-shock oscillations. Even though these oscillations are small in magnitude
Advanced numerical approximation of nonlinear …, 1998
In these lecture notes we describe the constraction, analysis, and applica-tion of ENO (Essential... more In these lecture notes we describe the constraction, analysis, and applica-tion of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essen-tially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are ...
In this paper the authors review some recent work on high-order well-balanced schemes. A characte... more In this paper the authors review some recent work on high-order well-balanced schemes. A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Well-balanced schemes satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. They
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