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.

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

For nearly incompressible elasticity, volumetric locking is a well-known phenomenon with low-order (cubic or lower) fi nite element method methods, of which continuous extended fi nite element methods (XFEMs) are no exception. We will present an XFEM that is simultaneously lock-free and optimally convergent. Based on our earlier work of an optimally convergent discontinuous-Galerkin-based XFEM,...

This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the Pk/Pk−1 (k ≥ 1) discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise Pl/Pk (l = k − 1, k) for the trace approximations of the velocity and pressure on the inter-element boundar...