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Commit b4961147 authored by Christian Engwer's avatar Christian Engwer
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[!456] [#137][doc] Add description for the TimeSteppingParameterInterface

Merge branch 'add_description_for_timesteppingparameterinterface' into 'master'

ref:pdelab/dune-pdelab Closes [#137]

See merge request [!456]

  [#137]: gitlab.dune-project.org/NoneNone/issues/137
  [!456]: gitlab.dune-project.org/pdelab/dune-pdelab/merge_requests/456


Closes #137
parents 01fd4a0e c77f1f35
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1 merge request!456[#137][doc] Add description for the TimeSteppingParameterInterface
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......@@ -17,6 +17,26 @@ namespace Dune {
*/
//! Base parameter class for time stepping scheme parameters
/**
* The parameters \f$ a,b \in \mathbb{R}^{s\times s+1} \f$ and
* \f$ d\in \mathbb{R}^d \f$ implement the generic class of time-stepping methods
* of Shu and Osher [1]:
* \f[
* \begin{aligned}
* u_h^{(0)} &= u_h^k\\
* \sum_{j=0}^s \left[ a_{ij} m_h\left(u_h^{(j)}, v; t^k + d_j\Delta t^k\right)
* + b_{ij}\Delta t^k r_h \left( u_h^{(j)},v,t^k+d_j\Delta t^k \right)\right] &= 0 & \forall i=1,\ldots,s \quad \forall v\in V_h(t^{k+1})\\
* u_h^{k+1} &= u_h^{(s)}
* \end{aligned}
* \f]
* where \f$ m_h\f$ is the temporal residual form (mass operator) and \f$
* r_h \f$ is the spatial residual form.
*
* This class in particular contains Runge-Kutta and fractional step
* methods. A more elaborate description can be found in the PDELab tutorials (tutorial03).
*
* [1] Chi W. Shu and Stanley Osher. Efficient implementation of essentially
* non- oscillatory shock-capturing schemes. J. Comput. Phys., 77:439–471
*
* \tparam R C++ type of the floating point parameters
*/
template<class R>
......
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