In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

Korn’s inequalities for piecewise H1 vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the threedimensional analysis of the pr...

Korn’s inequalities for piecewise H1 vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

A new approximate mortar condition is proposed for the lowest order CrouzeixRaviart finite element on nonmatching grids, which uses only the nodal values on the interface for the calculation of the mortar projection. This approach allows for improved and more flexible algorithms compared to those for the standard mortar condition where nodal values in the interior of a subdomain, those closest ...

We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we Laboratoire J. L. Lions (LJLL), University of Paris VI, Paris, France ([email protected]). Université de Liège, Institut Montefiore B28,...

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.