An introduction to Hybrid High-Order methods

Hybrid High-Order (HHO) methods are a class of new generation numerical schemes for PDEs with several advantageous features, including: 
(i) support of general polytopal meshes in arbitrary space dimension; 
(ii) arbitrary approximation order; 
(iii) compliance with the physics, including robustness with respect to the variations of physical coefficients and reproduction of key continuous properties at the discrete level; 
(iv) reduced computational cost thanks to hybridization, static condensation, and compact stencil. 
This presentation contains an introduction as well as examples of applications.