We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers' equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element so...

In the variational formulation of finite element models for mechanics problems, boundary conditions are classified as either essential or natural. The traction boundary conditions are identified as natural in many commonly-used finite element models. A valid finite element mode must satisfy explicitly the essential boundary conditions, since the latter are satisfied implicitly as a posteriori c...

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 ...

We present a parallel octree-based finite element method for large-scale earthquake ground motion simulation in realistic basins. The octree representation combines the low memory per node and good cache performance of finite difference methods with the spatial adaptivity to local seismic wavelengths characteristic of unstructured finite element methods. Several tests are provided to verify the...

There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized disp...

The occurrence of unphysical negative concentrations in solutions to diffusion equations is a well known and severe problem. Especially in three dimensions finite element discretizations give qualitatively very poor results, while finite volume discretizations are much more stable. We investigate the cause of these instabilities and trace them back to constraints on the mesh. It turns out that ...