Abstract In this paper, we discuss the superconvergence of “interpolated” collocation solutions for weakly singular Volterra integral equations second kind. Based on solution $$u_h$$ u h , two different interpolation postprocessing approximations higher accuracy: $$I_{2...

In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete...

Consider integration over the unit sphere in , especially when the integrand has singular behaviour in a polar region. In an earlier paper [4], a numerical integration method was proposed that uses a transformation that leads to an integration problem over the unit sphere with an integrand that is much smoother in the polar regions of the sphere. The transformation uses a grading parameter . Th...

Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar...

In this paper,we prove superconvergence results for the vector variable when lowest order triangular mixed nite elements of Raviart-Thomas type 17] on uniform triangulations are used, i.e., that the H(div;)-distance between the approximate solution and a suitable projection of the real solution is of higher order than the H(div;)-error. We prove results for both Dirichlet and Neumann boundary c...

In this paper, we study the superconvergence property for the discontinuous Galerkin (DG) and the local discontinuous Galerkin (LDG) methods, for solving one-dimensional time dependent linear conservation laws and convection-diffusion equations. We prove superconvergence towards a particular projection of the exact solution when the upwind flux is used for conservation laws and when the alterna...

Abstract. In this paper, the analysis of the superconvergence property of the discontinuous Galerkin (DG) method applied to one-dimensional time-dependent nonlinear scalar conservation laws is carried out. We prove that the error between the DG solution and a particular projection of the exact solution achieves (k+ 3 2 )-th order superconvergence when upwind fluxes are used. The results hold tr...

In this paper we investigate the superconvergence of local discontinuous Galerkin (LDG) methods for solving one-dimensional linear time-dependent fourth-order problems. We prove that the error between the LDG solution and a particular projection of the exact solution, ēu , achieves ( k+ 2 ) th-order superconvergence when polynomials of degree k (k 1) are used. Numerical experiments with Pk poly...

This paper derives sufficient conditions for supeconvergence of sums of bounded free random variables, and provides an estimate on the rate of su-