Discontinuous Skeletal Gradient Discretisation methods onpolytopal meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:355

Article

Di Pietro, Daniele A.¹  Droniou, Jerome²  Manzini, Gianmarco³ 

[1] Univ Montpellier, CNRS, Inst Montpellierain Alexander Grothendieck, Montpellier, France

[2] Monash Univ, Sch Math Sci, Melbourne, Vic, Australia

[3] Los Alamos Natl Lab, Appl Math & Plasma Phys Grp T5, Los Alamos, NM USA

关键词: Gradient discretisation methods;    Gradient schemes;    High-order Mimetic Finite Difference methods;    Hybrid High-Order methods;    Virtual Element methods;    Non-linear problems;   

DOI  :  10.1016/j.jcp.2017.11.018

来源: Elsevier

【 摘 要 】

In this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomials on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart-Thomas-Nedelec subspace. We prove that the novel DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free