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.