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On a global superconvergence of the gradient of linear triangular elements
Pekka NeittaanmäkiMichal Křížeksubject
Applied MathematicsMathematical analysisOrder of accuracySuperconvergenceglobal superconvergence for the gradientComputer Science::Numerical AnalysisGlobal superconvergence for the gradientMathematics::Numerical AnalysisNonlinear conjugate gradient methodElliptic curveComputational Mathematicserror estimatesNorm (mathematics)boundary fluxPiecewisepost-processing of the Ritz—Galerkin schemeGradient descentGradient methodMathematicsdescription
Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1987-05-01 | Journal of Computational and Applied Mathematics |