2019/04/30 by Alexandre Ern, Ern, Alexandre, Pietro Zanotti +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1904.13125
openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space L2(Ω). In this paper we devise and analyze a variant thereof, which is defined for any load in the dual Sobolev space H-1(Ω). The main feature of the present variant is that its H1-norm error can be bounded only in terms of the H1-norm best error in a space of broken polynomials. We establish this estimate with the help of recent results on the quasi-optimality of nonconforming methods. We prove also an improved error bound in the L2-norm by duality. Compared to previous works on quasi-optimal nonconforming methods, the main novelties are that Hybrid High-Order methods handle pairs of unknowns, and not a single function, and, more crucially, that these methods employ a reconstruction that is one polynomial degree higher than the discrete unknowns. The proposed modification affects only the formulation of the discrete right-hand side. This is obtained by properly mapping discrete test functions into H10(Ω).