Abstract Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge ...

In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, wh...

ture formulae on bounded convex regions in the plane. The construction is based on the behavior of spectra of certain multiplication operators and leads to nodes which are inside a prescribed convex region in R. The resulting interpolation schemes are numerically stable and the quadrature formulae have positive weights and almost (but not quite) optimal numbers of nodes. The performance of the ...

An edge-preserving method for image resizing (decimation and interpolation) is proposed. The decimation is considered as an orthogonal projection with respect to the chosen interpolation basis. The latter one is formed in a spline-like manner as a linear combination of B-splines of different degrees. This combination is optimized in such a way that the small image details are preserved. Conside...

We combine existing summation-by-parts discretization methods to obtain a simplified numerical framework for partial differential equations posed on complex multi-block/element domains. The interfaces (conforming or non-conforming) between blocks are treated with inner-product-preserving interpolation operators, and the result is high-order multi-block operator form that encapsulates both metri...

In this study, we propose a wavelet based speech data interpolation technique using the fractal characteristics of the speech. The aim of the method is to double the sampling rate, providing higher resolution while preserving the fractal characteristics of the speech signal. The method is applied to synthetic fractal signals and the results are compared with the linearly interpolated ones. Voic...

We obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip+ stability). A one-sided interpolation inequality between classical L1 error estimates and Lip+ stability bounds enables us to conv...

Interpolation by translates of a given radial basis function (RBF) has become a well-recognized means of tting functions sampled at scattered sites in R d. A major drawback of these methods is their inability to interpolate very large data sets in a numerically stable way while maintaining a good t. To circumvent this problem, a multilevel interpolation (ML) method for scattered data was presen...