The cell-vertex formulation of the finite volume method has been developed and widely used to model inviscid flows in aerodynamics: more recently, one of us has proposed an extension for viscous flows. The purpose of the present paper is two-fold: first we have applied this scheme to a well-known convection-diftusion model problem, involving flow round a 180° bend, which highlights some of the ...

This paper is concerned with collocation methods for one class of impulsive delay differential equations (IDDEs). Some results the convergence, global superconvergence and local are given. We choose a suitable piecewise continuous space to obtain high-order numerical methods. illustrative examples given verify theoretical results.

In this paper we give a complete analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for Volterra integral equations with constant delay. This analysis includes continuous collocation-based Volterra-Runge-Kutta methods as well as iterated collocation methods and their discretizations.

In this paper we study the existence of a formal series expansion of the error of spline Petrov–Galerkin methods applied to a class of periodic pseudodifferential equations. From this expansion we derive some new superconvergence results as well as alternative proofs of already known weak norm optimal convergence results. As part of the analysis the approximation of integrals of smooth function...

This paper deals with the convergence properties of the nonconforming quadrilateral Wilson element for a class of nonlinear parabolic problems in two space dimensions. Optimal H and L2 error estimates for the continuous time Galerkin approximations are derived. It is also shown for rectangular meshes that the gradient of the Wilson element solution possesses superconvergence, and that the Lx er...

Abstract In this paper, based on the continuous collocation polynomial approximations, we derive and analyse a class of trigonometric integrators for solving highly oscillatory hyperbolic system. The symmetry, convergence energy conservation approximations are rigorously analysed in details. Moreover, also proved that could achieve at superconvergence by choosing suitable points. Numerical expe...

Superconvergence in the L2-norm for the Galerkin approximation of the integral equation Lu = f is studied, where I is a strongly elliptic pseudodifferential operator on a smooth, closed or open curve. Let Uf, be the Galerkin approximation to u . By using the ^-operator, an operator that averages the values of uh , we will construct a better approximation than uh itself. That better approximatio...

Abstract Wave propagation problems arise in a wide range of applications. The energy conserving property is one of the guiding principles for numerical algorithms, in order to minimize the phase or shape errors after long time integration. In this paper, we develop and analyze a local discontinuous Galerkin (LDG) method for solving the wave equation. We prove optimal error estimates, superconve...

Based on the analysis of Cockburn et. al. [Math. Comp. 78 (2009), pp. 1-24] for a selfadjoint linear elliptic equation, we first discuss superconvergence results for nonselfadjoint linear elliptic problems using discontinuous Galerkin methods. Further, we have extended our analysis to derive superconvergence results for quasilinear elliptic problems. When piecewise polynomials of degree k ≥ 1 a...