In this paper, we study the convergence and superconvergence properties of the discontinuous Galerkin (DG) method for a linear convection-diffusion problem in one-dimensional setting. We prove that the DG solution and its derivative exhibit optimal O(h) and O(h) convergence rates in the L-norm, respectively, when p-degree piecewise polynomials with p ≥ 1 are used. We further prove that the p-de...

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Bénard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the sup...

In this paper we prove some superconvergence of a new family of mixed finite element spaces of higher order we introduced in [ETNA, Vol.37, pp.189–201, 2010]. Among all the mixed finite element spaces having optimal order of convergence on quadrilateral grids, this space has the smallest unknowns. However, the scalar variable is only suboptimal in general; thus we have employed a post-processin...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: MSC: 65D30 65D32 65R20 Keywords: Finite-part integral Composite midpoint rule Superconvergence Finite-part integral equation...

We consider mimetic finite difference approximations to second order elliptic problems on non-matching multi-block grids. Mortar finite elements are employed on the non-matching interfaces to impose weak continuity of the velocity. Optimal convergence and, for certain cases, superconvergence is established for both the scalar variable and the velocity.

The convergence analysis of the bilinear finite element method to a class of non-linear degenerate wave equation on anisotropic meshes is considered in this paper. Moreover, the global superconvergence for semidiscrete scheme is proposed through interpolation instead of the Ritz Volterra projection of the exact solution.