SundanceNitscheBC.hpp

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//                              Sundance
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#ifndef SUNDANCE_NITSCHEBC_H
#define SUNDANCE_NITSCHEBC_H

#include "SundanceDefs.hpp"
#include "SundanceExpr.hpp"


namespace Sundance
{
class CellFilter;
class QuadratureFamily;

/**
 * This function forms the expressions that apply the Dirichlet 
 * BC \f$u=u_{BC}\f$ via Nitsche's method for the Poisson operator.
 */
Expr NitschePoissonDirichletBC(int dim,
  const CellFilter& cells,
  const QuadratureFamily& quad,
  const Expr& kappa,
  const Expr& v,
  const Expr& u,
  const Expr& uBC,
  const double& gamma);

/**
 * This function forms the expressions that apply the Dirichlet 
 * BC \f${\bf u}={\bf u}_{BC}\f$ via Nitsche's method for the Stokes operator.
 * 
 * \param cells the surface on which the BC is to be applied
 * \param quad the quadrature rule to be used
 * \param nu the viscosity, which may be a function of velocity
 * \param v velocity test function
 * \param q pressure test function
 * \param u velocity unknown function
 * \param p pressure unknown function
 * \param uBC specified velocity at surface
 */
Expr NitscheStokesNoSlipBC(const CellFilter& cells,
  const QuadratureFamily& quad,
  const Expr& nu,
  const Expr& v,
  const Expr& q,
  const Expr& u,
  const Expr& p,
  const Expr& uBC,
  const double& gamma1,
  const double& gamma2
  );




}


#endif