Análisis de Von Neumann para el método Local Discontinuous Galerkin en 1D

• Castillo, Paul ^[1] ; Gómez, Sergio ^[2]
  1. [1] University of Puerto Rico System

     University of Puerto Rico System

     Puerto Rico

     
  2. [2] Universidad Nacional Autónoma de Honduras

     Universidad Nacional Autónoma de Honduras

     Honduras

     
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 37, Nº. 2, 2019 (Ejemplar dedicado a: Revista Integración, temas de matemáticas), págs. 199-217
• Idioma: español
• DOI: 10.18273/revint.v37n2-2019001
• Títulos paralelos:
  • Von Neumann analysis for the Local Discontinuous Galerkin method in 1D
• Enlaces
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• Resumen
  • español

    Utilizando el análisis de von Neumann como herramienta teórica,se desarrolla un análisis sobre las condiciones de estabilidad de algunosmétodos explícitos de avance en tiempo, en combinación con la discretización espacial Local Discontinuous Galerkin (LDG) por sus siglas en inglés y aproximaciones de alto orden. La constante de estabilidad CFL (Courant-Friedrichs-Lewy) se estudia en función de los parámetros del método LDG y el grado de aproximación. Se realiza una serie de experimentos numéricos para validar los resultados teóricos.

  • English

    Using the von Neumann analysis as a theoretical tool, an analysisof the stability conditions of some explicit time marching schemes, in combinationwith the spatial discretization Local Discontinuous Galerkin (LDG)and high order approximations, is presented. The stability constant, CFL(Courant-Friedrichs-Lewy), is studied as a function of the LDG parametersand the approximation degree. A series of numerical experiments is carriedout to validate the theoretical results.

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