We study the order of convergence Galerkin variational integrators for ordinary differential equations. approximate a (Lagrangian) problem by restricting space curves to set polynomials degree at most $s$ and approximating action integral using quadrature rule. show that, if rule is sufficiently accurate, thus obtained $2s$.

Superconvergence of the gradient for the linear simplicial finite-element method applied to elliptic equations is a well known feature in one, two, and three space dimensions. In this paper we show that, in fact, there exists an elegant proof of this feature independent of the space dimension. As a result, superconvergence for dimensions four and up is proved simultaneously. The key ingredient ...

This paper is concerned with superconvergence properties of the direct discontinuous Galerkin (DDG) method for one-dimensional linear convection-diffusion equations. We prove, under some suitable choice of numerical fluxes and initial discretization, a 2k-th and (k + 2) -th order superconvergence rate of the DDG approximation at nodes and Lobatto points, respectively, and a (k + 1) -th order of...

In this paper we consider superconvergence and supercloseness in the least-squares mixed finite element method for elliptic problems. The supercloseness is with respect to the standard and mixed finite element approximations of the same elliptic problem, and does not depend on the properties of the mesh. As an application, we will derive more precise a priori bounds for the least squares mixed ...

In Part I of this work, we analyzed superconvergence for piecewise linear finite element approximations on triangular meshes satisfying an O(h2) approximate parallelogram property. In this work, we consider superconvergence for general unstructured but shape regular meshes. We develop a postprocessing gradient recovery scheme for the finite element solution uh, inspired in part by the smoothing...

A technique of orthogonality correction in an element is introduced and applied to superconvergence analysis in finite element method. Ultraconvergence results for rectangular elements of odd degree n ≥ 3 are derived in the case of variable coefficients.

The phenomenon of superconvergence, first observed in the central limit theorem free probability, was subsequently extended to arbitrary laws for additive convolution. We show that same occurs multiplicative versions convolution on positive line and unit circle. also a certain Hölder regularity, demonstrated by Biane density with semicircular law, extends (additive multiplicative) convolutions ...

Higher order accuracy is one of the well-known beneficial properties discontinuous Galerkin (DG) method. Furthermore, many studies have demonstrated superconvergence property semi-discrete DG One can take advantage this by post-processing techniques to enhance solution. The smoothness-increasing accuracy-conserving (SIAC) filter a popular technique introduced Cockburn et al. (Math. Comput. 72(2...