(2000) Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/Finite Element ...

These lectures present a relatively recent introduction into the class of discontinuos Galerkin (DG) methods, named Discontinuous Petrov-Galerkin (DPG) methods. DPG methods, in which DG spaces form a critical ingredient, can be thought of as least-square methods in nonstandard norms, or as Petrov-Galerkin methods with special test spaces, or as a nonstandard mixed method. We will pursue all the...

A theorem providing a characterisation of Schwarzschildean initial data sets on slices with an asymptotically Euclidean end is proved. This characterisation is based on the proportionality of the Weyl tensor and its D’Alambertian that holds for some vacuum Petrov Type D spacetimes (e.g. the Schwarzschild spacetime, the C-metric, but not the Kerr solution). The 3+1 decomposition of this proporti...

A method for calculating special grid placement for three-point schemes which yields exponential superconvergence of the Neumann to Dirichlet map has been suggested earlier. Here we show that such a grid placement can yield impedance which is equivalent to that of a spectral Galerkin method, or more generally to that of a spectral Galerkin-Petrov method. In fact we show that for every stable Ga...

An adaptive mesh refuiement scheme and data shucture has been developed in conjunction with a streamline upwind Petrov-Galerkin finite element formulation for anaiysis of the semiconductor device equations. The nonlinear elecaostatic potential equation and convection dorninated camier current continuity equations are iteratively decoupled in the solution algorithm. Incremental continuation is e...