We consider the h-p Galerkin boundary element method applied to a weakly singular integral equation of the rst kind on an open curved surface. We focus on the eeective computation of the Galerkin matrix, i.e. we introduce a numerical qudrature rule which is shown (for a model case) to converge exponentially fast with the number of kernel evaluations. Numerical experiments show that the applicat...

In this paper, space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convectionreaction equation without control constraints is studied. Time discretization is performed by discontinuous Galerkin method with piecewise constant and linear polynomials, while symmetric interior penalty Galerkin with upwinding is used for spa...

We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitat...

A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a semiinfinite interval. By reformulating these equations with suitable functional transforms, it is shown that the Laguerre-Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre-Gal...

A collocation-Galerkin method is defined for Poisson's equation on the unit 2 square, using tensor products of continuous piecewise polynomials. Optimal L and Hq orders of convergence are established. This procedure requires fewer quadratures than the corresponding Galerkin procedure. Introduction. The collocation-Galerkin method was first introduced by Diaz [2], [3] for the two-point boundary ...

A new approach for analyzing cracked problems in 2D orthotropic materials using the well-known element free Galerkin method and orthotropic enrichment functions is proposed. The element free Galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. In this study, element free Galerkin is extrinsically enriched by the recently developed crack-tip orthot...

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...

We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time-dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf-sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propo...

A comparison of Standard Galerkin, Petrov–Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure–saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov–Galerkin method gives excellent results. ...