DUNE-ACFEM (unstable)
This model constructs from a given other model weak Dirichlet conditions as first introduced by [2]. More...
#include <dune/acfem/models/modules/nitschedirichletmodel.hh>
Public Member Functions | |
template<class Entity > | |
void | bind (const Entity &entity) |
Unbind from the previously bound entity. More... | |
void | unbind () |
Unbind from the previously bound entity. More... | |
template<class Intersection > | |
auto | classifyBoundary (const Intersection &intersection) |
Bind to the given intersection and classify the components w.r.t. More... | |
Detailed Description
class Dune::ACFem::PDEModel::NitscheDirichletBoundaryModel< Model, PenaltyFunction, Symmetrize >
This model constructs from a given other model weak Dirichlet conditions as first introduced by [2].
Following the somewhat easier-to-read presentation in [1] this model implement the following boundary contributions
\[ -\int_{\Gamma_D}\sigma(u,\nabla u)\cdot\nu\,\phi -\delta\,\int_{\Gamma_D}\big(\sigma(0,\,(u-g)\,\nu)-\sigma(0,\,0)\big)\cdot\nabla\phi +\int_{\Gamma_D}\mu\,(u-g)\,\phi \]
Here \(\sigma\) denotes the flux() method from the model, \(\delta > 0\) is some constant and \(\mu\) a suitable penalty parameter. \(u\) and \(\phi\) denote ansatz- and test-functions, respectively. \(g\) denotes the Dirichlet values.
For linear symmetric problems \(\delta\) can be chosen as -1
in order to keep the resulting model symmetric. If the model is linear asymmetric or even non-linear it is not so clear how to choose \(\delta\) in a suitable way.
The first boundary integral guarantees consistency of the method which leds to optimal convergence results if the penalty parameter \(\mu\) is chosen as \(\approx 1/h\) where h denotes the local mesh-size.
The respective parameters are passed as arguments to the constructor and/or generator function(s),
- See also
- nitscheDirichletBoundaryModel().
The documentation for this class was generated from the following file:
- dune/acfem/models/modules/nitschedirichletmodel.hh
