2020/08/12 by Stephen Metcalfe, Siva Nadarajah, Metcalfe, Stephen +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2008.05423
openalex publication_date 2020/08/12 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this work, we propose a new quasi-optimal test norm for a discontinuous\nPetrov-Galerkin (DPG) discretization of the ultra-weak formulation of the\nconvection-diffusion equation. We prove theoretically that the proposed test\nnorm leads to bounds between the target norm and the energy norm induced by the\ntest norm which are robust with respect to the diffusion parameter in the\nsolution and gradient components and have favorable scalings in the trace\ncomponents. We conclude with numerical experiments to confirm our theoretical\nresults.\n