• Home
  • UCSC journals portal
  • ANID repository
  • UCSC Thesis Repository
  • English
  • Español
  • Log In
    Have you forgotten your password?
  1. Home
  2. Productividad Científica
  3. Publicaciones Científicas
  4. Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frequency regime
 
Options
Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frequency regime
Dr. Barrios-Faúndez, Tomás 
Facultad de Ingeniería 
Bustinza, Rommel
Domínguez, Víctor
10.1016/j.cam.2015.12.024
Journal of Computational and Applied Mathematics
2016
We develop an a posteriori error analysis for Helmholtz problem using the local discontinuous Galerkin (LDG for short) approach. For the sake of completeness, we give a description of the main a priori results of this method. Indeed, under some assumptions on regularity of the solution of an adjoint problem, we prove that: (a) the corresponding indefinite discrete scheme is well posed; (b) the approach is convergent, with the expected convergence rates as long as the meshsize h is small enough. We give precise information on how small h has to be in term soft he size of the wave number and its distance to the set of eigenvalues for the same boundary value problem for the Laplacian. After that, we present a reliable and efficient a posteriori error estimator with detailed information on the dependence of the constants on the wave number. We finish presenting extensive numerical experiments which illustrate the theoretical results proven in this paper and suggest that stability and convergence may occur under less restrictive assumptions than those taken in the present work.
LDG
Helmholtz problem
Indefinite bilinear forms
Historial de mejoras
Proyecto financiado por: