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p_laplacian1.icc
Go to the documentation of this file.
#include "eta.h"
#include "nu.h"
#include "dirichlet.icc"
p_laplacian::p_laplacian (Float p1, const geo& omega, string approx)
: p(p1), Xh(), lh(), m(), pm(), a1(), pa1() {
Xh = space (omega, approx);
Xh.block ("boundary");
trial u (Xh); test v (Xh);
lh = integrate (v);
m = integrate (u*v);
pm = problem (m);
}
field p_laplacian::initial() const {
field uh (Xh, 0);
dirichlet (lh, uh);
return uh;
}
field p_laplacian::residue (const field& uh) const {
trial u (Xh); test v (Xh);
form a = integrate (compose(eta(p), norm2(grad(uh)))*dot(grad(u),grad(v)));
field mrh = a*uh - lh;
mrh.set_b() = 0;
return mrh;
}
void p_laplacian::update_derivative (const field& uh) const {
size_t d = Xh.get_geo().dimension();
trial u (Xh); test v (Xh);
a1 = integrate (dot(compose(nu<eta>(eta(p),d), grad(uh))*grad(u),grad(v)));
pa1 = problem (a1);
}
field p_laplacian::derivative_solve (const field& rh) const {
field delta_uh (Xh,0);
pa1.solve (rh, delta_uh);
return delta_uh;
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
p_laplacian::a1
form a1
Definition p_laplacian.h:42
p_laplacian::Xh
space Xh
Definition p_laplacian.h:38
p_laplacian::derivative_solve
field derivative_solve(const field &mrh) const
Definition p_laplacian1.icc:55
p_laplacian::pa1
problem pa1
Definition p_laplacian.h:43
p_laplacian::p_laplacian
p_laplacian(Float p, const geo &omega, string approx)
Definition p_laplacian1.icc:28
p_laplacian::lh
field lh
Definition p_laplacian.h:39
p_laplacian::m
form m
Definition p_laplacian.h:40
p_laplacian::initial
field initial() const
Definition p_laplacian1.icc:37
p_laplacian::update_derivative
void update_derivative(const field &uh) const
Definition p_laplacian1.icc:49
p_laplacian::residue
field residue(const field &uh) const
Definition p_laplacian1.icc:42
p_laplacian::pm
problem pm
Definition p_laplacian.h:41
problem
see the problem page for the full documentation
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
dirichlet.icc
The Poisson problem with homogeneous Dirichlet boundary condition – solver function.
dirichlet
void dirichlet(const field &lh, field &uh)
Definition dirichlet.icc:25
eta.h
The p-Laplacian problem – the eta function.
d
size_t d
Definition neumann-laplace-lambda.cc:28
nu.h
The p-Laplacian problem – the nu function.
eta
Definition eta.h:25
nu
Definition nu.h:26
p
Definition sphere.icc:25
u
Definition leveque.h:25