We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra is implemented as an extension to the domain-specific language UFL, the Unified Form Language. This allows users to construct many finite element spaces beyon...

After a short introduction to Generalized Finite Element Methods (GFEM) for two-dimensional triangular elements, a technique is presented to impose Dirichlet-type boundary conditions to global higher order GFEM ansatz spaces. The convergence rates of h-, p-, hp-and enriched p-versions of the GFEM are discussed with respect to singularities. The method is applied to a two dimensional Poisson mod...

Triangular sets appear under various names in many papers concerning systems of polynomial equations. Ritt (1932) introduced them as characteristic sets. He described also an algorithm for solving polynomial systems by computing characteristic sets of prime ideals and factorizing in field extensions. Characteristic sets of prime ideals have good properties but factorization in algebraic extensi...

Novel Multi-dimensional Upwind Constrained Transport (MUCT) schemes on un-structured triangular grids are described. Constrained Transport (CT) discretizations conserve the divergence-free nature of divergence-free vector fields on the discrete level. Multi-dimensional Upwind (MU) schemes generalize the concept of dimensionally split upwind schemes for hyperbolic systems to truly multidimension...

Most computer contour mapping of irregularly spaced data points is performed using an intermediate rectangular grid. An alternative method is proposed whereby a map area is automatically divided into suitable triangular domains with a data point at each vertex. Surface estimation and contour plotting are then performed independently for each triangle using a measured or bestfit plane associated...

T h i s paper describes C A B O T , a case-based syst e m t h a t is able to ad jus t i ts re t r ieva l and adapt a t i o n met r ics , in a d d i t i o n to s to r ing cases. I t has been app l ied to the game of OTHELLO. Exper iments show t h a t C A B O T saves a b o u t ha l f as many cases as s imi la r systems t h a t do no t ad jus t the i r re t r ieva l and a d a p t a t i o n mechani...

In this paper we present a new unstructured spectral element method for use on triangular and tetrahedral subdomains. The algorithm maintains the accuracy and efficiency of standard quadrilateral/hexahedral spectral element methods but offers greater adaptivity. Standard unstructured meshes can be used and the order of the polynomial expansion can be varied within each triangular/tetrahedral su...