TY - GEN
T1 - A review of hybrid high-order methods
T2 - International Conference on Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, 2014
AU - Di Pietro, Daniele A.
AU - Ern, Alexandre
AU - Lemaire, Simon
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns attached to mesh faces and cells (hence, the term hybrid), and these unknowns are polynomials of arbitrary order k ≥ 0 (hence, the term highorder). HHO methods are devised from local reconstruction operators and a local stabilization term. The discrete problem is assembled cellwise, and cell-based unknowns can be eliminated locally by static condensation. HHO methods support generalmeshes, are locally conservative, and allowfor a robust treatment of physical parameters in various situations, e.g., heterogeneous/anisotropic diffusion, quasiincompressible linear elasticity, and advection-dominated transport. This paper reviews HHO methods for a variable-diffusion model problem with nonhomogeneous, mixed Dirichlet–Neumann boundary conditions, including both primal and mixed formulations. Links with other discretization methods from the literature are discussed.
AB - Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns attached to mesh faces and cells (hence, the term hybrid), and these unknowns are polynomials of arbitrary order k ≥ 0 (hence, the term highorder). HHO methods are devised from local reconstruction operators and a local stabilization term. The discrete problem is assembled cellwise, and cell-based unknowns can be eliminated locally by static condensation. HHO methods support generalmeshes, are locally conservative, and allowfor a robust treatment of physical parameters in various situations, e.g., heterogeneous/anisotropic diffusion, quasiincompressible linear elasticity, and advection-dominated transport. This paper reviews HHO methods for a variable-diffusion model problem with nonhomogeneous, mixed Dirichlet–Neumann boundary conditions, including both primal and mixed formulations. Links with other discretization methods from the literature are discussed.
UR - https://www.scopus.com/pages/publications/84992731084
U2 - 10.1007/978-3-319-41640-3_7
DO - 10.1007/978-3-319-41640-3_7
M3 - Conference contribution
AN - SCOPUS:84992731084
SN - 9783319416380
T3 - Lecture Notes in Computational Science and Engineering
SP - 205
EP - 236
BT - Building Bridges
A2 - Georgoulis, Emmanuil H.
A2 - Barrenechea, Gabriel R.
A2 - Brezzi, Franco
A2 - Cangiani, Andrea
A2 - Georgoulis, Emmanuil H.
PB - Springer Verlag
Y2 - 8 July 2014 through 16 July 2014
ER -