On the Convergence of Finite-Element Approximations of a Relaxed Variational Problem

The accuracy of finite-element approximations to a convex, but not strictly convex, variational problem is considered. Convergence is proved for a finite-element approximation of a particular vector field related to the solution. In a special one-dimensional case, 0(h) convergence is shown for a pie...

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Veröffentlicht in:SIAM journal on numerical analysis 1990-04, Vol.27 (2), p.419-436
1. Verfasser: French, Donald A.
Format: Artikel
Sprache:eng
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Zusammenfassung:The accuracy of finite-element approximations to a convex, but not strictly convex, variational problem is considered. Convergence is proved for a finite-element approximation of a particular vector field related to the solution. In a special one-dimensional case, 0(h) convergence is shown for a piecewise linear approximation of the derivative. h denotes the size of each element domain. Numerical results are also presented for this one-dimensional case.
ISSN:0036-1429
1095-7170
DOI:10.1137/0727025