Getfem++ User Guide

• Introduction
• How to install
• Build a mesh
• • Add an element to a mesh
  • Remove an element from a mesh
  • Simple structured meshes
  • Mesh regions
  • Methods of the getfem::mesh object
  • Using dal::bit_vector
  • Face numbering
  • Save and load meshes
  • • From getfem file format
    • Import a mesh
• Selecting finite element methods
• • Examples
  • Other methods of the mesh_fem object
  • Obtaining generic mesh_fems
• Selecting integration methods
• • Methods of the mesh_im object
• Mesh refinement
• Linear algebra procedures
• Standard assembly procedures
• • Laplacian (Poisson) problem
  • Linear Elasticity problem
  • Stokes Problem with mixed finite element method
  • Assembling a mass matrix
• Compute arbitrary elementary matrices - generic assembly procedures
• Incorporate new finite element methods in getfem++ 
• Incorporate new approximated integration methods in getfem++ 
• Level-sets, Xfem, fictitious domains
• • Representation of level-sets
  • Mesh cut by level-sets
  • Adapted integration methods
  • Discontinuous field across some level-sets
  • Fictitious domain approach with Xfem
• Support for Xfem methods
• Interpolation of a finite element method on non-matching meshes
• • mixed methods with different meshes
  • mortar methods
• Compute L² and H¹ norms
• Compute derivatives
• Export and view a solution
• • Saving mesh and mesh_fem objects for the Matlab interface
  • Producing mesh slices
  • Exporting mesh, mesh_fem or slices to VTK
  • Exporting mesh, mesh_fem or slices to OpenDX
• Interpolation on different meshes
• The model bricks
• • The model state variable
  • Basic properties of a brick
  • Brick parameters
  • generic elliptic brick
  • Source term brick
  • Constraint brick
  • Dirichlet condition brick
  • Example of a complete Poisson problem
  • Predefined solvers
  • Isotropic linearized elasticity brick
  • Qu term brick
  • Helmholtz brick
  • linear incompressibility (or nearly incompressibility) brick
  • Small displacement plasticity brick
  • Contact and friction conditions brick
  • Linearized plate brick
  • Large strain elasticity brick
  • Large strain incompressibility brick
• Parallelization of getfem++ 
• Catch errors
• Example : Laplacian program
• Appendix A. Finite element method list
• • Dof graphical codification
  • Classical P_K Lagrange elements on simplices
  • Classical Lagrange elements on other geometries
  • Elements with hierarchical basis
  • • Hiercarchical elements with respect to the degree
    • Composite elements
    • Hierarchical composite elements
  • Classical vectorial elements
  • • Raviart-Thomas of lowest order elements
    • Nedelec (or Whitney) edge elements
  • Specific elements in dimension 1
  • • GaussLobatto element
    • Hermite element
    • Lagrange element with an additional bubble function
  • Specific elements in dimension 2
  • • Elements with additional bubble functions
    • Non-conforming P₁ element
    • Hermite element
    • Morley element
    • Argyris element
    • Hsieh-Clough-Tocher element
    • A composite C¹ element on quadrilaterals
  • Specific elements in dimension 3
  • • Elements with additional bubble functions
    • Hermite element
• Appendix B. Cubature method list
• • Exact Integration methods
  • Newton cotes Integration methods
  • Gauss Integration methods on dimension 1
  • Gauss Integration methods on dimension 2
  • Gauss Integration methods on dimension 3
  • Direct product of integration methods
  • Composite integration methods
• References
• Index

Compute L² and H¹ norms

The file getfem/getfem_assembling.h defines the functions to compute L² and H¹ norms of a solution. The following functions compute the different norms
 

 getfem::asm_L2_norm(mim, mf, U);
 getfem::asm_H1_semi_norm(mim, mf, U);
 getfem::asm_H1_norm(mim, mf, U);

where mim is a getfem::mesh_im used for the integration, mf is a getfem::mesh_fem and describes the finite element method on which the solution is defined, U is the vector of values of the solution on each degree of freedom of mf. The size of U should be mf.nb_dof().

In order to compare two solutions, it is often simpler and faster to use the following function than to interpolate one mesh_fem on another:  

getfem::asm_L2_dist(mim, mf1, U1, mf2, U2);
getfem::asm_H1_dist(mim, mf1, U1, mf2, U2);  

These functions return the L² and H¹ norms of u₁ - u₂.