Related papers: ENO reconstruction and ENO interpolation are stabl…
We review the currently available stability properties of the ENO reconstruction procedure, such as its monotonicity and non-oscillatory properties, the sign property, upper bounds on cell interface jumps and a total variation-type bound.…
In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell…
A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to…
Embedded WENO methods utilize all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for…
Cases have shown that WENO schemes usually behave robustly on problems containing shocks with high pressure ratios when uniformed or smooth grids are present, while nonlinear schemes based on WENO interpolations might relatively be liable…
We propose a third-order WENO reconstruction which satisfies the sign property, required for constructing high resolution entropy stable finite difference scheme for conservation laws. The reconstruction technique, which is termed as…
A new Essentially Non-oscillatory (ENO) recovery algorithm is developed and tested in a Finite Volume method. The construction is hinged on a reformulation of the reconstruction as the solution to a variational problem. The sign property of…
Image zooming or upsampling is a widely used tool in image processing and an essential step in many algorithms. Upsampling increases the number of pixels and introduces new information into the image, which can lead to numerical effects…
The $\ell_2-$ and $\ell_1-$regularized modified Lagrange interpolation formulae over $[-1,1]$ are deduced in this paper. This paper mainly analyzes the numerical characteristics of regularized barycentric interpolation formulae, which are…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the…
We present a novel arbitrary high order accurate central WENO spatial reconstruction procedure (CWENO) for the solution of nonlinear systems of hyperbolic conservation laws on fixed and moving unstructured simplex meshes in two and three…
A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially…
On semiconductor growth surfaces, surface reconstructions appear. Estimation of the reconstructed structures is essential for understanding and controlling growth phenomena. In this study, the stability of a mixture of two different surface…
A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
This paper presents a generalized ENO (GENO)-type nonlinear reconstruction scheme for compressible flow simulations. The proposed reconstruction preserves the accuracy of the linear scheme while maintaining essentially non-oscillatory…
We propose an alternative reconstruction for weighted essentially non-oscillatory schemes with adaptive order (WENO-AO) for solving hyperbolic conservation laws. The alternative reconstruction has a more concise form than the original…
Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In this work, we present a non-separable progressive multivariate…