We present a technique to couple finite element and finite sphere discretizations. The finite elements and finite spheres are coupled with full displacement compatibility. We also present a technique in which a finite element discretization is enriched with finite spheres. We consider two-dimensional conditions and present solutions to illustrate the analysis procedures. 2005 Elsevier Ltd. All ...

A simple finite element method for the Reissner–Mindlin plate model in the primitive variables is presented and analyzed. The method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation, with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging. ...

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal order interpolation for the velocity and pressure fields. Finally, we show by counterexample ...

We present a family of conforming finite elements for the Stokes problem on general triangular meshes in two dimensions. The lowest order case consists of enriched piecewise linear polynomials for the velocity and piecewise constant polynomials for the pressure. We show that the elements satisfy the inf-sup condition and converges optimally for both the velocity and pressure. Moreover, the pres...

Mafic rocks including basalts and gabbros are the main constituents of Birjand ophiolites. They are found in several places and show low grade metamorphism in the field and under the microscope. Chondrite-normalized REE patterns for basalts and gabbros indicate that these rocks are transitional-enriched to depleted mid-oceanic ridge basalts respectively. Otherwise, N-MORB normalized trace eleme...