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Analysis of a continuous finite element method for hyperbolic equations. (English) Zbl 0619.65100

A finite element method for the problem \(\alpha \cdot \nabla u+\beta u=f\) in \(\Omega\) on the inflow boundary \(\Gamma_{in}(\Omega)\), where \(\alpha\) is a unit vector and \(\Omega\) is a bounded polygonal domain in \(R^ 2\), is analyzed. The method is applicable over a triangulation of the domain, and produces a continuous piecewise polynomial approximation which can be developed from triangle to triangle. For n-th degree approximation, the errors in the approximate solution and its gradient are shown to be at least of order \(h^{n+1/4}\) and \(h^{n-1/2}\), respectively, assuming sufficient regularity in the solution.
Reviewer: I.P.Ialamov

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems
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