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Journal of Scientific Computing

Erschienen in:

01.01.2021

High Order Finite Difference Multi-resolution WENO Method for Nonlinear Degenerate Parabolic Equations

verfasst von: Yan Jiang

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2021

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Abstract

In this paper, we propose a new finite difference weighted essentially non-oscillatory (WENO) scheme for nonlinear degenerate parabolic equations which may contain non-smooth solutions. An alternative formulation is designed to approximate the second derivatives in a conservative form. In this formulation, the odd order derivatives at half points are used to construct the numerical flux, instead of the usual practice of reconstruction. Moreover, the multi-resolution WENO scheme is designed to circumvent the negative ideal weights and mapped nonlinear weights that appear when applying the standard WENO idea. We will describe the scheme formulation and present numerical tests for one- and two-dimensional, demonstrating the designed high order accuracy and non-oscillatory performance of the schemes constructed in this paper.

Vorheriger Artikel Lax-Wendroff Approximate Taylor Methods with Fast and Optimized Weighted Essentially Non-oscillatory Reconstructions

Nächster Artikel Convergence of Adaptive Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

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Titel: High Order Finite Difference Multi-resolution WENO Method for Nonlinear Degenerate Parabolic Equations
verfasst von: Yan Jiang
Publikationsdatum: 01.01.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01382-y

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