An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. (English) Zbl 0747.65082
The aim of this paper is to introduce and analyze a new alternating direction implicit (ADI) Galerkin method for hyperbolic initial-boundary value problems. It has at least two advantages over the earlier similar methods: First, it involves only two time levels, so variable time steps can be used, and second, the initial conditions can be determined (imposed) in a very natural way. Optimal a priori \(H^ 1_ 0\)- and \(L^ 2\) error estimates are carried out in a standard way.
Reviewer: C.I.Gheorghiu (Cluj-Napoca)
MSC:
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
65F10 | Iterative numerical methods for linear systems |
35L15 | Initial value problems for second-order hyperbolic equations |