We derive some basic properties for a class of discretely divergence free nite elements. These make possible a new proof of the smoothing property in a standard multigrid algorithm for the Stokes equations. In addition with appropriate divergence-free grid transfer routines of second order accuracy we get the full multigrid convergence. We demonstrate how to develop and implement eeciently thes...

A very simple and eÆcient nite element method is introduced for two and three dimensional viscous incompressible ows using the vorticity formulation. The method relies on recasting traditional nite element method in the spirit of the high order accurate nite di erence methods introduced by the authors in [10]. Optimal accuracy of arbitrary order can be achieved using standard nite element or sp...

A simple upper bound on the size of nite subgroups of GL(n; Z) is given. Only elementary number-theoretic arguments are used, thereby avoiding previous methods depending on estimates of the Jordan number and the classiication of nite simple groups.

Suppose thatM is an in nite structure with nite relational vocabulary such that every relation symbol has arity at most 2. IfM is simple and homogeneous then its complete theory is supersimple with nite SU-rank which cannot exceed the number of complete 2-types over the empty set.

Using a combinatorial theorem of Herwig on extending partial isomorphisms of relational structures, we give a simple proof that certain classes of algebras, including Crs, polyadic Crs, and WA, have thè`nite base property' and have decidable universal theories, and that any nite algebra in each class is representable on a nite set.

Three simple mesh examples are presented to show that neither Delaunay nor strictly non-obtuse mesh elements are required for a nite element computation. Mesh requirements based on a recent condition given in literature are investigated to guarantee certain properties of the resulting stiiness matrix. The experiments are conducted using a general nite element and nite volume solver.

By studying dressing orbits a complete account is given of the (full) super-horizontal holomorphic maps of nite type from the 2-plane into a full ag manifold. It is shown that precisely one dressing orbit contains all 2-spheres of nite type. From this follows a simple description of all harmonic 2-spheres in CP n of nite type.

the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.