A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (Ye and Zhang (2020)). Removing stabilizers from discontinuous methods simplifies formulations reduces programming complexity. The purpose is to introduce a new WG without that convergence rates one order higher than optimal rates. This the first achieves superconvergence mes...

In this paper, the global superconvergence analysis for the finite element approximation of the distributed optimal control governed by Stokes equations is discussed. For the control, a global superconvergence result is derived by applying patch recovery technique. For the state and the co-state, the global superconvergence results are derived by applying some postprocessing techniques for the ...

In this paper, we will present a review of the multistep collocation method for Delay Volterra Integral Equations (DVIEs) from [1] and then, we study the superconvergence analysis of the multistep collocation method for DVIEs. Some numerical examples are given to confirm our theoretical results.

We consider a singularly perturbed convection-diffusion boundary value problem whose solution contains exponential and characteristic layers. The is numerically solved by the FEM SDFEM method with bilinear elements on graded mesh. For we prove almost uniform convergence superconvergence. use of mesh allows for to yield estimates in SD norm, which not possible Shishkin type meshes. Numerical res...

In this paper we study the convergence of a centred finite difference scheme on a non-uniform mesh for a 1D elliptic problem subject to general boundary conditions. On a non-uniform mesh, the scheme is, in general, only first-order consistent. Nevertheless, we prove for s ∈ (1/2, 2] order O(hs)-convergence of solution and gradient if the exact solution is in the Sobolev space H1+s(0, L), i.e. t...

This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs ensures stability of the methods. The solution can be computed element by element with optimal order of convergence k+ 1 in the L2 norm and superconvergence...

In this paper, an analysis of the accuracy-enhancement for the discontinuous Galerkin (DG) method applied to one-dimensional scalar nonlinear hyperbolic conservation laws is carried out. This requires analyzing the divided difference of the errors for the DG solution. We therefore first prove that the [Formula: see text]-th order [Formula: see text] divided difference of the DG error in the [Fo...

In this work, the bilinear finite element method on a Shishkin mesh for convection-diffusion problems is analyzed in the two-dimensional setting. A superconvergence rate O(N−2 ln N + N−1.5 lnN) 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 ind...

In this paper, we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify right-hand side of body force in discrete formulation exploiting divergence preserving velocity reconstruction operator, which is crux pressure-independent error estimates. The optimal convergence gradient,...