期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 355, 期 -, 页码 397-425出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.11.018
关键词
Gradient discretisation methods; Gradient schemes; High-order Mimetic Finite Difference methods; Hybrid High-Order methods; Virtual Element methods; Non-linear problems
资金
- ANR grant HHOMM [ANR-15-CE40-0005]
- ARC [DP170100605]
- Laboratory Directed Research and Development program, under the National Nuclear Security Administration of the U. S. Department of Energy by Los Alamos National Laboratory [DE-AC52-06NA25396]
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.
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