2022/01/05 by Nestor Sánchez, Sánchez, Nestor, Tonatiuh Sánchez-Vizuet +3 · 2 citations
Engineering · Mathematics · #65N15 #65N30 #65R20 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2201.01395
openalex publication_date 2022/01/05 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In their article "Coupling at a distance HDG and BEM", Cockburn, Sayas and Solano proposed an iterative coupling of the hybridizable discontinuous Galerkin method (HDG) and the boundary element method (BEM) to solve an exterior Dirichlet problem. The novelty of the numerical scheme consisted of using a computational domain for the HDG discretization whose boundary did not coincide with the coupling interface. In their article, the authors provided extensive numerical evidence for convergence, but the proof of convergence and the error analysis remained elusive at that time. In this article we fill the gap by proving the convergence of a relaxation of the algorithm and providing a priori error estimates for the numerical solution.