On the approximation of derivative values using a WENO algorithm with progressive order of accuracy close to discontinuities

Abstract

In this article, we introduce a new WENO algorithm that aims to calculate an approximation to derivative values of a function in a non-regular grid. We adapt the ideas presented in [Amat et al., SIAM J. Numer. Anal. (2020)] to design the nonlinear weights in a manner such that the order of accuracy is maximum in the intervals close to the discontinuities. Some proofs, remarks on the choice of the stencils and explicit formulas for the weights and smoothness indicators are given. We also present some numerical experiments to confirm the theoretical results.

Document Details

Document Type
Pub Defense Publication
Publication Date
Sep 01, 2022
Source ID
10.1007/s40314-022-02004-z

Entities

People

  • Chi-Wang Shu
  • Dionisio F. Yáñez
  • Juan Ruiz-álvarez
  • Sergio Amat

Organizations

  • Air Force Office of Scientific Research
  • Fundación Seneca
  • Ministry of Science, Technology and Telecommunications of Costa Rica
  • National Science Foundation

Tags

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.