Aspects of Trefftz’ Method in BEM and FEM and their coupling
نویسندگان
چکیده
In both boundary element methods and Trefftz-type finite element methods a partial differential equation in some domain is treated by solving a discrete problem on the boundary of the domain and possibly the boundaries between subdomains. We consider a Trefftz element formulation which is based on the complementary energy functional, and we compare different regularizations of the interelement continuity conditions. Also starting from the complementary energy functional, mixed finite elements can be constructed such that the stresses satisfy equilibrium a priori. We describe a coupling of these elements with the by now classical symmetric Galerkin-BEM.
منابع مشابه
Stiffeners Mechanical Effect Analysis by Numerical Coupling
Given any structure, we seek to find the solution of mechanical problem as precisely and efficiently as possible. Within this condition, the BEM is robust and promising development, standing out in the analysis of cases with occurrence of large stress gradients, as in problems of fracture mechanics. Moreover, in BEM the modeling of infinite means is performed naturally, without the use of appro...
متن کاملConvection-adapted BEM-based FEM
We present a new discretization method for homogeneous convectiondiffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness matrices are constructed by means of local boundary element techniques. Our method, which we refer to as a BEM-based FEM, can therefore be considered a local ...
متن کاملOn the Adaptive Coupling of Finite Elements and Boundary Elements for Elasto-Plastic Analysis
The purpose of this paper is to present an adaptive FEM-BEM coupling method that is valid for both twoand three-dimensional elasto-plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub-domains in the standard FEM-BEM coupling approaches. The method estima...
متن کاملApplication of Boundera Element Method (Bem) to Two-Dimensional Poisson's Eqation
BEM can be used to solve Poisson's equation if the right hand side of the equation is constant because it can easily be transformed to an equivalent Laplace equation. However, if the right hand side is not constant, then such a treatment is impossible and part of the equation can not be transformed over the boundary, hence, the whole domain has to be discretized. Although this takes away impor...
متن کاملA posteriori error estimates for the Johnson–Nédélec FEM–BEM coupling
Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work,...
متن کامل