a constitutive model based on two–dimensional unstructured galerkin finite volume method (gfvm) is introduced and applied for analyzing nonlinear behavior of cracked concrete structures in equilibrium condition. the developed iterative solver treats concrete as an orthotropic nonlinear material and considers the softening and hardening behavior of concrete under compression and tension by using...

The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—fi...

The multi-scale-finite-volume (MSFV) procedure for the approximate solution of elliptic problems with varying coefficients has been recently modified by introducing an iterative loop to achieve any desired level of accuracy (iterative MSFV, IMSFV). We further develop the iterative concept considering a Galerkin approach to define the coarse-scale problem, which is one of the key elements of the...

In this paper, we consider the issue of convergence toward entropy solutions for high order finite volume weighted essentially non-oscillatory (WENO) scheme and discontinuous Galerkin (DG) finite element method approximating scalar nonconvex conservation laws. Although such high order nonlinearly stable schemes can usually converge to entropy solutions of convex conservation laws, convergence m...

In [19, 20, 22], we constructed uniformly high order accurate discontinuous Galerkin (DG) which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. The technique also applies to high order accurate finite volume schemes. In this paper, we show an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (E...

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...

Bending analysis of FGM plates under uniform and sinusoidal loaded result in forth order partial differential equation. In this paper the analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure is derived using the Galerkin method. The solution was develope based on the classical plate’s theory (CLPT). The reliability ...

This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin met...

In order to perform accurate electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, the so-called EEG forward problem. Therefore, it is necessary to apply numerical methods that are able to take the individual geometr...

An algorithm and essential subroutines programs are presented which implement two stage finite element Galerkin method for integrating the complete two dimensional horizontal flow model. In this method high accuracy is obtained by combining the Galerkin product with a high-order difference approximation to derivatives in the nonlinear advection operator. Program includes the use of a weighted s...