dune-fem  2.4.1-rc
Modules | Classes
Local Discontinous Galerkin for first order hyperbolic equations
Collaboration diagram for Local Discontinous Galerkin for first order hyperbolic equations:

Modules

 Limiting operation
 

Classes

class  Dune::Fem::LocalMassMatrixImplementation< DiscreteFunctionSpace, VolumeQuadrature >
 Local Mass Matrix inversion implementation, select the correct method in your implementation. More...
 
class  Dune::Fem::LocalMassMatrix< DiscreteFunctionSpace, VolumeQuadrature >
 Local Mass Matrix for arbitrary spaces. More...
 
class  Dune::Fem::LocalMassMatrixImplementationDgOrthoNormal< DiscreteFunctionSpace, VolumeQuadrature >
 DG Local Mass Matrix for arbitrary spaces. More...
 
class  Dune::Fem::LocalDGPass< DiscreteModelImp, PreviousPassImp, passIdImp >
 
class  Dune::Fem::DGDiscreteModelCaller< DiscreteModel, Argument, PassIds >
 model caller for local DG pass More...
 

Detailed Description

**

Description: Solver for equations of the form

\begin{eqnarray*} v + div(f(x,u)) + A(x,u)\nabla u &=& S(x,u) \quad\mbox{in}\quad \Omega \\ \end{eqnarray*}

where $ u $ is the argument and $ v $ is computed. Weak formulation on a cell T:

\[ \int_T v \phi = -\int_{\partial T} g \phi + \int_T f \cdot \nabla \phi + \int_T Q \phi \]

with $ g \approx f \cdot n + \tilde{A}[u] \cdot n $ and $ Q \approx S - A \nabla u $ where $ \tilde{A} $ denotes the arithmetic average and $ [u] $ the jump of $ u $ over the cell interface.\ The discrete model provides the analyticalFlux f, the source Q and the numericalFlux g.