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| template<class Entity , class Point > |
| void | flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const |
| | Evaluate \(A(x, u)\nabla u(x)\) in local coordinates. More...
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| template<class Entity , class Point > |
| void | linearizedFlux (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const |
| | Evaluate the linearized flux in local coordinates. More...
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| template<class Entity , class Point > |
| void | fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, RangeType &result) const |
| | Compute the point-wise value of the flux-part of the operator, meaning the part of the differential operator which is multiplied by the derivative of the test function. More...
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| void | setEntity (const Entity &entity) const |
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| bool | setIntersection (const Intersection &intersection) const |
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| void | source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const |
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| void | linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const |
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| void | robinFlux (const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const |
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| void | linearizedRobinFlux (const RangeType &uBar, const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const |
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const ExpressionType & | expression () const |
| | Return a const reference to the underlying expression.
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ExpressionType & | expression () |
| | Return a mutable reference to the underlying expression.
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ExpressionType | operator* () const |
| | Return a copy from of the underlying expression.
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template<class FunctionSpace>
class Dune::ACFem::P_LaplacianOperatorParts< FunctionSpace >
The p-Laplacian-model.
The flux-terms has the form
\[
\int_\Omega |\nabla U|^{p-2}\,\nabla U : \nabla \phi\quad\forall \phi
\]
where \(U\) is the unknown und \(ß\phi\) denotes the test functions. This is the formal first variation of the functional
\[
U\mapsto \int_\Omega |\nabla U|^p = \int_\Omega (\nabla U : \nabla U)^{p/2}.
\]
FIXME: use rather the following for the vector valud case?
\[
U\mapsto \int_\Omega \sum_{i=1}^r (\nabla U_i\cdot\nabla U_i)^{p/2}.
\]
The second form yields a component-wise uncoupled p-Laplacian, the first yields a coupled version. We implement here the first, but this may not be what you want.
- Bug:
- This is totally untested. Cross check before using and then remove the comment.
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