Projects per year
Abstract
In this work, we prove optimal W^{s,p}approximation estimates (with p ∈ [1,+∞]) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont–Scott approximation theory together with two novel abstract lemmas: An approximation result for bounded projectors, and an L^{p}boundedness result for L^{2}orthogonal projectors on polynomial subspaces. The W^{s,p}approximation results have general applicability to (standard or polytopal) numerical methods based on local polynomial spaces. As an illustration, we use these W^{s,p}estimates to derive novel error estimates for a Hybrid HighOrder (HHO) discretisation of Leray–Lions elliptic problems whose weak formulation is classically set in W^{1,p}(Ω) for some p ∈ (1,+∞). This kind of problems appears, e.g. in the modelling of glacier motion, of incompressible turbulent flows, and in airfoil design. Denoting by h the meshsize, we prove that the approximation error measured in a W^{1,p}like discrete norm scales as
h^{k+1}_{p−1} when p ≥ 2 and as h^{(k+1)(p−1)} when p < 2.
Original language  English 

Pages (fromto)  879908 
Number of pages  30 
Journal  Mathematical Models and Methods in Applied Sciences 
Volume  27 
Issue number  5 
DOIs  
Publication status  Published  2017 
Keywords
 (Formula presented.)approximation properties of elliptic projector on polynomials
 (Formula presented.)Laplacian
 error estimates
 Hybrid HighOrder methods
 nonlinear elliptic equations
Projects
 1 Finished

Discrete functional analysis: bridging pure and numerical mathematics
Droniou, J., Eymard, R. & Manzini, G.
Australian Research Council (ARC), Monash University, Université ParisEst Créteil Val de Marne (ParisEast Créteil University Val de Marne), University of California System
1/01/17 → 31/12/20
Project: Research