Superconvergence results for linear triangular elements

TL;DR: In this paper, the authors studied the superconvergence of m-degree triangular finite element solution and its average gradient at symmetric points for a second order elliptic problem and showed that there are no other superconversgence points independent of the coefficients of elliptic equation.

TL;DR: In this article, the finite element method for non-smooth elliptic equations is studied and error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis.

TL;DR: In this article, the role of mesh quality on the accuracy of linear finite element approximation was studied, which showed explicitly how the shape and size of elements, and symmetry structure of mesh effect on the error of numerical approximation.

TL;DR: In this article, the error in approximating the exact solution via the finite element method baised upon linear elements has been studied and a direct sup-norm estimate in terms of a modulus of continuity of the solution has been derived.

TL;DR: In this article, the concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced, and the relationship between local smoothing and the reduced integration technique is established.

TL;DR: In this article, the authors studied the superconvergence phenomenon when solving a 2nd order elliptic problem by the usual linear elements and showed that the convergence rate of the averaged gradient to an exact gradient in the L 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.

TL;DR: In this article, a simple schema simple for determining the gradients a partir de l'approximation a elements finis triangulaires lineaire par morceaux de la solution d'un probleme elliptique du second ordre.

TL;DR: In this paper, the super convergence of the gradient of approximate solutions to second order elliptical équations is analyzed and justified for a large ciass of curved isoparametric quadrilatéral éléments.