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On the accuracy of the finite element method plus time relaxation. (English) Zbl 1201.65168

The authors apply the finite elements method (FEM) to the advection equation
\[ u_{t}+ \overrightarrow{a} \nabla{u}=f,\qquad x\in \Omega,\qquad t\in (0,T] \]
in the case when \( u = \overline{u}+ u'\), where \(\overline{u} \) is a special average of \(u\) and \(u'\) is an associated fluctuation. In this case a better accuracy is obtained by the FEM.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems

Software:

FreeFem++
PDFBibTeX XMLCite
Full Text: DOI

References:

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