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Least-squares finite elements for first-order hyperbolic systems. (English) Zbl 0641.65080
This paper is a continuation of the authors’ work on the least-squares finite element method. Several interpretations and alternative derivations are given to show that this scheme is equivalent to upwind Petrov-Galerkin schemes and Taylor-type Galerkin schemes. Stability analysis shows that it is unconditionally stable as against the Taylor- Galerkin method with regard to the Courant number. The error estimate is easily derived by appropriate comparison. It is further extended to scalar nonlinear equation in conservative form. Comparative numerical results are given for the linear case and for the inviscid Burgers’ equation. The authors indicate possibilities for further work.
Reviewer: V.Subba Rao

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems
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