Space

Secondly, the Finite Element space must be set on the computational mesh. One of the following is typically used (including setting of Dirichlet boundary conditions):

// H1 Space.
// Polynomial order.
int POLYNOMIAL_ORDER = 3;

// Initialize boundary conditions.
// This is a custom (derived) boundary condition. More about this in the section
// 'Object model - deriving your own specialized classes'.
CustomDirichletCondition bc_essential(
  std::vector<std::string>({"Bottom", "Inner", "Outer", "Left"}),
  BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);

// Initialize the container to pass the boundary conditions to the Space.
EssentialBCs<double> bcs(&bc_essential);

// Create an H1 space.
SpaceSharedPtr<double> space(new H1Space<double>(mesh, &bcs, POLYNOMIAL_ORDER));

// HCurl Space.
// Polynomial order.
int POLYNOMIAL_ORDER = 5;

// Initialize boundary conditions.
Hermes::Hermes2D::DefaultEssentialBCConst<std::complex<double> > bc_essential
(std::vector<std::string>({"Corner_horizontal", "Corner_vertical"}), 0);
EssentialBCs<std::complex<double> > bcs(&bc_essential);

// Create an Hcurl space.
SpaceSharedPtr<std::complex<double> > space(new HcurlSpace<std::complex<double> >(mesh, &bcs, POLYNOMIAL_ORDER));

// HDiv Space. This example does not use any Dirichlet boundary conditions.
int POLYNOMIAL_ORDER = 2;
SpaceSharedPtr<double> space(new HdivSpace<double>(mesh, POLYNOMIAL_ORDER));

// L2 Space. This Space does not take any boundary conditions which corresponds to the
// fact that the FE space is a space of discontinuous functions.
// If we for example use polynomial order = 0, we use just piecewise
// constant basis functions.
SpaceSharedPtr<double> space(new L2Space<double>(mesh, 0));

More about spaces can be found in the ‘hermes-tutorial’ documentation, section ‘A-linear’, chapter ‘02-space’ and in the Doxygen documentation.

More about Dirichlet boundary conditions can be found in the ‘hermes-tutorial’ documentation, section ‘A-linear’, chapter ‘04-bc-dirichlet’, and for defining a non-constant custom boundary condition, see the chapter ‘07-general’.