We show a superconvergence property for the Semi-Lagrangian Discontinuous Galerkin scheme of arbitrary degree in the case of constant linear advection equation with periodic boundary conditions.

In this article, we propose a novel discontinuous Galerkin method for convectiondiffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable and competitive with the main existing methods for these problems. The second is that, when the method uses polynomial approximations of the same degree for bot...

We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property: max P∈S |(∇u−∇uh)(P)| = O(h2)| lnh|, where ∇uh(P) denotes the average gradient on elements cont...

<p style='text-indent:20px;'>This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates include all cases Abel-type Firstly, existence, uniqueness and continuous dependence on true solution under local Lipschitz condition linear growth are d...

In this work, we report on an ongoing project to implement an hp-adaptive finite element method. The inspiration of this work came from the development of certain a posteriori error estimates for high order finite elements based on superconvergence Bank and Xu [2003a,b], Bank et al. [2007]. We wanted to create an environment where these estimates could be evaluated in terms of their ability to ...

We consider conforming finite element approximation of fourth-order singularly perturbed problems of reaction diffusion type. We prove superconvergence of standard C1 finite element method of degree p on a modified Shishkin mesh. In particular, a superconvergence error bound of ( N−1ln(N + 1))p in a discrete energy norm is established. The error bound is uniformly valid with respect to the sing...