In this paper, we consider the time dependent Maxwell’s equations in dispersive media on a bounded three-dimensional domain. Global superconvergence is obtained for semi-discrete mixed finite element methods for three most popular dispersive media models: the isotropic cold plasma, the one-pole Debye medium, and the two-pole Lorentz medium. Global superconvergence for a standard finite element ...

Some collocation schemes used to solve mth order ordinary differential equations are known to display superconvergence at the mesh points. Here we show that some such schemes have additional superconvergence points for the approximate solution and all of its derivatives. Using such points, we argue that a mesh selection scheme introduced by Dodson can be expected to perform well under general c...

The lowest order Raviart-Thomas rectangular element is considered for solving the singular perturbation problem ?div(arp) + bp = f; where the diagonal tensor a = (" 2 ; 1) or a = (" 2 ; " 2): Global uniform convergence rates of O(N ?1) for both p and a 1=2 rp in the L 2-norm are obtained in both cases, where N is the number of intervals in both directions. The pointwise interior (away from the ...

In this work, we present a two-dimensional mixed-hybrid nite element model of variably saturated ow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT 0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations. Theroretical superconvergence properties of the R...

In this paper, we propose a new stabilizer-free and pressure-robust weak Galerkin finite element method for the Stokes equations with superconvergence on polytopal mesh in primary velocity-pressure formulation. Convergence rates one order higher than optimal velocity both energy norm $L^2$-norm pressure are proved our proposed scheme. The $H$(div)-preserving operator has been constructed based ...

Semidiscrete mixed nite element approximation to parabolic initial boundary value problems is introduced and analyzed Superconvergence estimates for both pressure and velocity are obtained The estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in L and data in Hr for r su ciently large Because of the smoothing prop...

We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the L-orthogonal projection onto the approximate space for a numerical trace into all facet integrals in the usual HDG formulation. The orders of convergence for all variables are optimal if we use polynomials of degree k + l, k + 1 and k, where k...

A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...

A semidiscrete mixed nite element approximation to parabolic initial-boundary value problems is introduced and analyzed. Superconvergence estimates for both pressure and velocity are obtained. The estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in L 2 and data in H r , for r suuciently large. Because of the smoo...

We present new a priori error analyses of the coupling of the Raviart–Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary vari...