×

On high-order radiation boundary conditions. (English) Zbl 0864.65065

Engquist, Bjorn (ed.) et al., Computational wave propagation. Based on the IMA workshop, Minneapolis, MN, USA 1994/95. New York, NY: Springer. IMA Vol. Math. Appl. 86, 1-21 (1997).
Summary: We develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Padé approximants proposed by B. Engquist and A. Majda [Math. Comput. 31, 629-651 (1977; Zbl 0367.65051) and Commun. Pure Appl. Math. 32, 313-357 (1979; Zbl 0396.76066)] lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.
For the entire collection see [Zbl 0855.00031].

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite