## 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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