estimator::ImplicitResidual< F > Class Template Referenceabstract
Abstract class representing the implicit residual a posteriori error estimator. More...
#include <implicitResidual.hh>
Public Member Functions | |
| void | addBoundaryData (const concepts::Set< uint > &nSet, const concepts::ElementFormula< F > &g) |
| Add boundary informations (i.e. More... | |
| void | addBoundaryData (const concepts::Set< uint > &rSet, const concepts::ElementFormula< F > &h1, const concepts::ElementFormula< F > &h2) |
| Add boundary informations (i.e. More... | |
| virtual ImplicitResidual< F > * | clone () const =0 |
Protected Member Functions | |
| ImplicitResidual (const concepts::SpaceOnCells< F > &spc, const concepts::Vector< F > &sol) | |
| Constructur of the explicit residual a posteriori error estimator. More... | |
| virtual std::ostream & | info (std::ostream &os) const |
Protected Attributes | |
| concepts::Set< uint > | eAttrbs_ |
| concepts::Sequence< const concepts::ElementFormula< F > * > | g_ |
| concepts::Sequence< concepts::Set< uint > > | gAttrbs_ |
Detailed Description
template<class F>
class estimator::ImplicitResidual< F >
Abstract class representing the implicit residual a posteriori error estimator.
At the moment just one underlying space is supported, i.e. with that robin conditions cannot be handeled for the residuals, atm
This uses the flux approximation proposed by Bank and Weise, that is
n_k \cdot [\mathcal{A} Grad(u)] = 0.5 \cdot n_K ( \mathcal{A}Grad[u_h]_{|K} + \mathcal{A}Grad[u_h]_{K'} )
where n_k is the outer normal on a cell K, and (K, K') are neighboured Elements.
Definition at line 37 of file implicitResidual.hh.
Constructor & Destructor Documentation
◆ ImplicitResidual()
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inlineprotected |
Constructur of the explicit residual a posteriori error estimator.
The input residual is builded outside the class. For given elliptic PDE Lu = f, res = f - L(u_h), where u_h is the FEM approximation.
Example: L = -Laplace + c(x)*ID, use hp2D::Functions as Laplacian, Value and ParsedFormulas
- Parameters
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spc Underlying 2d Space, i.e. a AdaptiveSpace sol solution vector of the approximated FEM solution res strong Residual.
Definition at line 125 of file implicitResidual.hh.
Member Function Documentation
◆ addBoundaryData() [1/2]
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inline |
Add boundary informations (i.e.
on point/edge/face) to build boundary residuals on a given requested set of edges through edge attributes.
This applicates i.e for Neumann b.c. :
Let the boundary condition be of the form :
n^T * [A*Grad(u)] = g
Then the L2 edge residual representation has the form :
![\[ || g - n_e^T * [A*Grad(u_{hp})] ||_{L^2(e)} \]](form_288.png)
where n_e is the outward pointing normal vector, that comes from the underlying element that has edge e.
Definition at line 64 of file implicitResidual.hh.
◆ addBoundaryData() [2/2]
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inline |
Add boundary informations (i.e.
on point/edge/face) to build boundary residuals of the form
![\[ h2 + h1 * u_{hp} \]](form_289.png)
on a given set of edge attributes, where u_{hp} is the trace of the hp-fem solution on the requested edges. This applicates i.e. for Robin b.c. :
Let the boundary condition be of the form :
n^T * [A*Grad(u)] = h1 * u + h2
Then the L2 edge residual representation has the form :
![\[ || h1 * u_{hp} + h2 - n_e^T * [A*Grad(u_{hp})] ||_{L^2(e)} \]](form_290.png)
where n_e is the outward pointing normal vector, that comes from the underlying element that has edge e.
Definition at line 98 of file implicitResidual.hh.
◆ clone()
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pure virtual |
Implemented in estimator::ImplicitResidual2D< F >.
◆ info()
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inlineprotectedvirtual |
Reimplemented in estimator::ImplicitResidual2D< F >.
Definition at line 129 of file implicitResidual.hh.
Member Data Documentation
◆ eAttrbs_
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protected |
Definition at line 148 of file implicitResidual.hh.
◆ g_
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protected |
Definition at line 142 of file implicitResidual.hh.
◆ gAttrbs_
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protected |
Definition at line 144 of file implicitResidual.hh.
The documentation for this class was generated from the following file:
- estimator/implicitResidual.hh