In this paper, we study a bybridizable discontinuous Galerkin (HDG) method for the numerical solution of 2D time-harmonic Maxwell’s equations. The formulations are given, and the relationship between the HDG scheme and the upwind flux DG method is also examined. The presented numerical results show the effectiveness of the proposed HDG method especially in comparison to the upwind flux DG metho...

Meshfree methods have been formulated based on Galerkin type weak formulation and collocation type strong formulation. The approximation functions commonly used in the Galerkin based meshfree methods are the moving least-squares (MLS) and reproducing kernel (RK) approximations, while the radial basis functions (RBFs) are usually employed in the strong form collocation method. Galerkin type form...

(1) A one-dimensional minimization problem and the Ritz method. (2) Weak formulation and the Galerkin method. Abstract error estimates. (3) The lemma of variations. Euler-Lagrange equations. Weak formulation, again. (4) The Ritz-Galerkin finite element method: philosophy. (5) The piecewise linear finite element space and basis functions. The linear system. (6) The piecewise linear finite elemen...

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modi cat...

Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and medicine. They can be considered as ordinary differential equations in sequence spaces. In this work, a fully adaptive algorithm for the computational treatment of such systems is developed. The method combines time discretization with extrapolation in Hilbert spaces with a discrete Galerki...

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

In this pat)er we introduce a high order discontinuous Galerkin method for two dimensional incoinpressible flow in vorticity streamfunction fornnllation. The inonlentuni equation is treated exl)licitly, utilizing the efficiency of the discontimtous Galerkin method. The streanlflmction is obtained by a standard Poiss(m solver using (:ontinu(lus finite elenmnts. There is a natural matching betwee...