finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

In this paper, we consider sampling in a reproducing kernel subspace of L. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-proje...

We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions which guarantee that the continuous problem defines a dissipative dynamical system. We show that, under certain conditions, the discontinuous Galerkin approximation also defines a dissipative dynamical system and we ...

In this paper we provide estimates to the rate of convergence of the nonlinear Galerkin approximation method. In particular, and by means of an illustrative example, we show that the nonlinear Galerkin method converges faster than the usual Galerkin method.

This paper presents the application of the Successive Galerkin Approximation (SGA) to the Hamilton-Jacobi-Bellman equation to obtain solutions of the optimal attitude control problem. Galerkin's method approximates the value function by a truncated Galerkin series expansion. To do so a truncated Galerkin basis set is formed. A suucient number of functions must be included in this Galerkin basis...

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...

In this paper a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces H. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. N...

This paper considers two aspects of the nonlinear H∞ control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs Equation (HJIE) that arises in the output feedback case. Design of nonlinear H∞ controllers obtained by Taylor approximation an...

Zusammenfassung Dieser Beitrag behandelt die Approximation linearer verteilt-parametrischer Systeme zweiter Ordnung mittels eines Galerkin-Ansatzes. Das resultierende endlich-dimensionale Approximationsmodell besitzt ebenfalls die Struktur zweiter Ordnung und ist wie das Originalsystem asymptotisch stabil und passiv. Es wird gezeigt, wie die Freiheitsgrade der Galerkin-Approximation zu wählen s...

In the present paper, we discuss the superconvergence of the interpolated Galerkin solutions for Hammerstein equations. With the interpolation post-processing for the Galerkin approximation xh, we get a higher order approximation I 2r−1 2h xh, whose convergence order is the same as that of the iterated Galerkin solution. Such an interpolation post-processing method is much simpler than the iter...