Ultra-weak formulation of a hypersingular integral equation on polygons\n and DPG method with optimal test functions

2013/09/06 by Norbert Heuer, Heuer, Norbert, Felipe Pinochet +1
Engineering · Mathematics · Physics and Astronomy · #65N12 #65N30 #65N38 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1309.1697

openalex publication_date 2013/09/06 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28

Abstract

We present an ultra-weak formulation of a hypersingular integral equation on\nclosed polygons and prove its well-posedness and equivalence with the standard\nvariational formulation. Based on this ultra-weak formulation we present a\ndiscontinuous Petrov-Galerkin method with optimal test functions and prove its\nquasi-optimal convergence in L². Theoretical results are confirmed by\nnumerical experiments on an open curve with uniform and adaptively refined\nmeshes.\n

Related

• Discontinuous Petrov-Galerkin boundary elements
• A Space-Time DPG Method for the Heat Equation
• A time-stepping DPG scheme for the heat equation
• On the coupling of DPG and BEM
• An analysis of the practical DPG method