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Summation by parts, projections, and stability. II. (English) Zbl 0848.65064
[For part I see ibid. 64, No. 211, 1035-1065; Supplement S23–S26 (1995; Zbl 0828.65111).]
The author considers the stability of high-order finite difference approximations of parabolic and symmetric hyperbolic systems of partial differential equations, paying particular attention to the boundary conditions. The problems created by having to approximate at corners are discussed and energy estimates for solutions are given. The ideas discussed are extended to the case of inhomogeneous boundary data by means of an example, and compatibility conditions are given.

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
35M10 PDEs of mixed type
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[1] Heinz-Otto Kreiss and Jens Lorenz, Initial-boundary value problems and the Navier-Stokes equations, Pure and Applied Mathematics, vol. 136, Academic Press, Inc., Boston, MA, 1989. · Zbl 0689.35001
[2] Pelle Olsson, Summation by parts, projections, and stability. I, Math. Comp. 64 (1995), no. 211, 1035 – 1065, S23 – S26. · Zbl 0828.65111
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