Stable spectral methods on tetrahedral elements. (English) Zbl 0959.65112

Hesthaven, J. S.; Teng, C. H.

SIAM J. Sci. Comput. 21, No. 6, 2352-2380 (2000).

The authors present a framework for the construction of stable spectral methods on arbitrary domains with unstructured grids. They identify nodal sets suitable for polynomial interpolation on a tetrahedron and formulate stable spectral schemes on such unstructured nodal sets. They also discuss the efficient computation of derivatives and the stability of the discrete schemes.

Reviewer: J.D.P.Donnelly (Oxford)

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws
34A34	Nonlinear ordinary differential equations and systems
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
65L60	Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations

Keywords:

spectral methods; asymptotic stability; penalty methods; tetrahedral elements