A systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial C0 finite elements in a three-dimensional setting. This identification is based upon explicitly constructing an orthogonal decomposition of local finite element spaces. Derivative and function value superconvergence points are investigated for both the Poisson and the Laplace equ...

JYV ASKYL A 1996 2 Superconvergence for second order triangular mixed and standard nite elements. Abstract In this paper we will prove that both the second order Raviart-Thomas type mixed nite elements and the quadratic standard nite elements on regular and uniform triangular partitions, are superconvergent with respect to Fortin interpolation. This result implies the superconvergence for quadr...

We invenstigate a local analysis of the Lavrentiev regularization method applied to the ill-posed Cauchy problem. A convergence analysis of the approximated solution is carried out in a sub region away from the incomplete boundary, which is the source of the instability of the Cauchy solution. The use of a Carleman estimate with boundary condition by D.Tataru (see [4]) brings about super-conver...

We identify and study an LDG-hybridizable Galerkin method, which is not an LDGmethod, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuousGalerkinmethods using polynomials of degree k ≥ 0 for both the potential as well as the flux, the order of convergence in L of both unknowns is k + 1. Moreover, both the ap...

This article is concerned with the numerical computation of homoclinic solutions converging to a hyperbolic or semi-hyperbolic equilibrium of a system _ u = f(u; ). The approximation is done by replacing the original problem by a boundary value problem on a nite interval and introducing an additional phase condition to make the solution unique. Numerical experiments have indicated that the para...

In this paper, we present a super-convergence result for the Local Discontinuous Galerkin method for a model elliptic problem on Cartesian grids. We identify a special numerical ux for which the L 2-norm of the gradient and the L 2-norm of the potential are of order k + 1=2 and k + 1, respectively, when tensor product polynomials of degree at most k are used; for arbitrary meshes, this special ...

This paper is the second of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed. In this paper, we focus on how the lack of consistency introduced by the nonuniformity of the grids in uences the convergence of ux-splitting monotone schemes to the entropy solution. We obtain the optimal rate of convergence of ( x)1=2 in L1(L1) for consistent...

In this work, the bilinear nite element method on a Shishkin mesh for convection-diiusion problems is analyzed in the two-dimensional setting. A su-perconvergence rate O(N ?2 ln 2 N + N ?1:5 ln N) in a discrete-weighted energy norm is established under certain regularity assumptions. This convergence rate is uniformly valid with respect to the singular perturbation parameter. Numerical tests in...

In this paper we study the global convergence of the implicit residual-based a posteriori error estimates for a discontinuous Galerkin method applied to one-dimensional linear hyperbolic problems. We apply a new optimal superconvergence result [Y. Yang and C.-W. Shu, SIAM J. Numer. Anal., 50 (2012), pp. 3110-3133] to prove that, for smooth solutions, these error estimates at a fixed time conver...

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in R. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in W (Ω) and Lp(Ω), for 2 ...