r3.06.14 Introduction to Hybrid High-Order Methods (HHO)

Summary:

This document presents HHO methods for problems in nonlinear mechanics (small and large deformations) and linear and non-linear thermal mechanics. The corresponding keywords in AFFE_MODELE for mechanical models in code_aster are D_ PLAN_HHO and 3D_ HHO. An extension to non-local formulations is possible (D_ PLAN_GRAD_HHO and 3D_ GRAD_HHO). For thermal, there are AXIS_HHO, PLAN_HHO and 3D_ HHO. It is then necessary to choose between the formulations LINEAIRE and QUADRATIQUE.

More complete theoretical details are given in [1] and [9].

Table of contents

• 1. Introduction
• 2. Description of the method
  • 2.1. The case of linear elasticity
  • 2.2. Discreet frame
  • 2.3. Local reconstruction and stabilization operators
  • 2.4. Discreet global problem HHO
• 3. Implementation
  • 3.1. Unknowns HHO and numbering
  • 3.2. Dirichlet boundary conditions
  • 3.3. Post-treatment
  • 3.4. Scope of use
• 4. Bibliography