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• Hybrid Discontinuous Galerkin method for perturbations of the modified Helmholtz equation

  D. Azofeifa, M. Moreles

  SMCCA (2025). 3

  
  

  Abstract

  The application of the Discontinuous Galerkin Method to elliptic problems usually leads to underdetermined linear systems, and penalization or suitable constraints are necessary. In this work, we address this issue for the modified Helmholtz equation. For this elliptic problem, we propose a hybrid numerical flux in the Discontinuous Galerkin method to introduce unknowns on the edges of the mesh, yielding a well-determined linear system. Performance is tested as a Poisson solver. Additionally, accurate approximations are presented for certain Helmholtz problems in Coastal Ocean Modeling.

  Abstract
  The application of the Discontinuous Galerkin Method to elliptic problems usually leads to underdetermined linear systems, and penalization or suitable constraints are necessary. [...]

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