An Introduction to --adaptive Finite Element Method

• 1 Introduction
  • 1.1 Variational formulation
  • 1.2 Finite element approximation
  • 1.3 Shape functions in linear element
  • 1.4 Adaptive terminology
• 2 -adaptivity
  • 2.1 Regularity requirements.
  • 2.2 Unrefinements
  • 2.3 Constrained nodes.
  • 2.4 Propagation of the constraints.
  • 2.5 Solution after adaptation.
  • 2.6 Assembly of unconstrained element matrices.
  • 2.7 Elimination of constraints.
  • 2.8 Penalty enforcement of constraints.
  • 2.9 Quality of refined mesh.
• 3 -adaptivity.
  • 3.1 Hierarchical shape functions
  • 3.2 2-dimensional elements
  • 3.3 Irregular elements, serendipity.
  • 3.4 Continuity requirements.
  • 3.5 Information from error estimator for -adaptivity
  • 3.6 Solution after adaptation.
  • 3.7 Boundary conditions for -meshes
• 4 --adaptivity.
  • 4.1 Continuity requirements.
  • 4.2 hp constraint on the edge
  • 4.3 Adaptivity strategy (-versus-).
• 5 Special problems in 3d case.
  • 5.1 Mesh regularity.
  • 5.2 --constraints.
  • 5.3 Deadlocks