Summary
For piecewise linear Ritz approximation of second order elliptic Dirichlet problemsAu=f over domainsΩ⊂ℝn globalL ∞ error boundsO(h 2|lnh|v) are obtained under the assumptionfεL ∞(Ω). The proof rests on interpolation ofH 2(Ω)-functions with second derivatives in the space of John and Nirenberg by piecewise linear splines and a technique of Nitsche [7] using weighted Sobolev norms.
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Diese Note wurde verfaßt mit der Unterstützung des Sonderforschungsbereiches 72 der DFG, Bundesrepublik Deutschland
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Rannacher, R. Zur L∞-Konvergenz linearer finiter Elemente beim Dirichlet-Problem. Math Z 149, 69–77 (1976). https://doi.org/10.1007/BF01301633
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DOI: https://doi.org/10.1007/BF01301633