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 apply our proposed early parallel adaptive computing methodology for numerical solution of semiconductor device equations with triangular meshing technique. This novel simulation based on adaptive triangular mesh, finite volume, monotone iterative, and a posteriori error estimation methods, is developed and successfully implemented on a Linux-cluster with message passing inter...

Nonpolynomial finite element methods for Helmholtz problems have seen much attention in recent years in the engineering and mathematics community. The idea is to use instead of standard polynomials Trefftz-type basis functions that already satisfy the Helmholtz equation, such as plane waves [17], Fourier-Bessel functions [8] or fundamental solutions [4]. To approximate the inter-element interfa...

We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to ...

The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG met...

The aim of this paper is to compare some recent numerical schemes for solving hyperbolic conservation laws. We consider the flux vector splitting finite volume methods, finite volume evolution Galerkin scheme as well as the discontinuous Galerkin scheme. All schemes are constructed using time explicit discretization. We present results of numerical experiments for the shallow water equations fo...

Heat transfer phenomena of flat plate solar collector filled with different nanofluids has been investigated numerically. Galerkin’s Finite Element Method is used to solve the problem. Heat transfer rate, average bulk temperature, average sub-domain velocity, outlet temperature, thermal efficiency, mean entropy generation and Bejan number has been investigated by varying the solid nanoparticle ...

The subject of the paper is the derivation and analysis of third order nite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the rst order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation ~ U n = RhU n 2 S h from the piecewise constantU 2 S h , to feed into ...

In this paper, we present a positivity-preserving high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for compressible Euler equations based on the framework for constructing uniformly high order accurate positivity-preserving discontinuous Galerkin and finite volume schemes for Euler equations proposed in [20]. The major advantages of the HWENO schemes is their...

Abstract. We extend a well-balanced finite volume evolution Galerkin (FVEG) method to nonuniform grids. As a model problem, we consider the two-dimensional shallow water equations with a source term modelling the bottom topography. Our work is based on the well-balanced scheme proposed in (Lukáčová, Noelle, Kraft, J.Comp.Physics, 221, 2007). We present selected test cases to demonstrate the cap...