Stable spectral methods for conservation laws on triangles with unstructured grids
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Classical digital signal processing (DSP) lore tells us the tale of a continuous-time primeval signal, of its brutal sampling, and of the magic sinc interpolation that, under the aegis of bandlimitedness, brings the original signal back to (continuous) lif ...
This paper addresses the problem of interpolating signals defined on a 2-d sphere from non-uniform samples. We present an interpolation method based on locally weighted linear and nonlinear regression, which takes into account the differences in importance ...
We present a simple but generalized interpolation method for digital images that uses multiwavelet-like basis functions. Most of interpolation methods uses only one symmetric basis function; for example, standard and shifted piecewise-linear interpolations ...
The sampling and interpolation of a sound field in two and three dimensions along a circle is discussed. The Fourier domain representation of the sound field is used, and an angular sampling theorem is developed for the sampling of the sound field along a ...
We investigate stabilized Galerkin approximations of linear and nonlinear convection-diffusion-reaction equations. We derive nonlinear streamline and cross-wind diffusion methods that guarantee a discrete maximum principle for strictly acute meshes and fir ...
An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and it ...
We present a simple, original method to improve piecewise linear interpolation with uniform knots: We shift the sampling knots by a fixed amount, while enforcing the interpolation property. Thanks to a theoretical analysis, we determine the optimal shift t ...
We prove a priori anisotropic estimates for the L2 and H1 interpolation error on linear finite elements. The full information about the mapping from a reference element is employed to separate the contribution to the elemental error c ...
A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equa ...
We review the current state of Fourier and Chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations. Throughout the discussion we emphasize recent develop ...