A preliminary study of p-refinement with vector finite elements is reported. Results suggest that improved accuracy can be obtained from representations employing a mixture of polynomial orders instead of a uniform polynomial order. Results also suggest that it might be possible to jump directly from the local error in a p=0 expansion to a final representation employing 5 or more polynomial ord...

A new O(n) algorithm is given for evaluating univariate polynomials of degree n in the P olya basis. Since the Lagrange, Bernstein, and monomial bases are all special instances of the P olya basis, this technique leads to e cient evaluation algorithms for these special bases. For the monomial basis, this algorithm is shown to be equivalent to Horner's rule. 1 P olya basis functions Let nk(t) be...

We propose an appropriate and eÆcient multiresolution visualization method for so called h{p{adaptive nite element data. This is done by generalizing the method of adaptive projection, recently introduced by the authors, to function data of piecewise higher polynomial degree on locally re ned grids. Given some suitable error indicators, we eÆciently extract a continuous h{p{adaptive projection ...

Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by uncertainty in their parameters. The polynomial chaos method is a computational approach to solve stochastic partial differential equations (SPDE) by projecting the solution onto a space of orthogonal polynomials of the stochastic variables and solving for the deterministic coeffi...

Birkhoff (or lacunary) interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about function and its derivatives. A Birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space. In this paper we split up the initial problem in subproblems having a unique polynomial solution and use multino...

Standard spectral codes for full sphere dynamics utilize a combination of spherical harmonics and suitableradial basis to represent fluid variables. These functions have rotational invariance not present ingeophysical flows. Gyroscopic alignment - along the axis rotation is ahallmark geophysical fluids in rapidly rotating regime. The Taylor-Proudman theorem, resultingfrom dominant balance Corio...

In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite smoothness. In this paper we deliver a first error estimates for the multilevel algorithm using analytic basis functions. The estimate has two parts, one in...

The prediction of lithology is necessary in all areas of petroleum engineering. This means that to design a project in any branch of petroleum engineering, the lithology must be well known. Support vector machines (SVM’s) use an analytical approach to classification based on statistical learning theory, the principles of structural risk minimization, and empirical risk minimization. In this res...