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Finite volume approximations and strict stability for hyperbolic problems. (English) Zbl 0985.65103

Summary: Strictly stable finite volume formulations for long time integration of hyperbolic problems are formulated by modifying conventional and widely used finite volume schemes close to the boundary. The modification leads to difference operators that satisfy a summation-by-parts rule and the boundary conditions are imposed by a penalty procedure. Both node centered and cell centered approximations are considered. Numerical studies corroborate the superior stability of the modified formulations for long time integrations.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems

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