stokes_dirichlet_dg.icc

The Stokes problem with Dirichlet boundary condition by the discontinuous Galerkin method – solver function

void stokes_dirichlet_dg (const space& Xh, const space& Qh,
form& a, form& b, form& c, form& mp, field& lh, field& kh,
integrate_option iopt = integrate_option())
{
size_t k = Xh.degree();
size_t d = Xh.get_geo().dimension();
Float beta = (k+1)*(k+d)/Float(d);
trial u (Xh), p (Qh);
test v (Xh), q (Qh);
a = integrate (2*ddot(Dh(u),Dh(v)), iopt)
+ integrate ("sides", beta*penalty()*dot(jump(u),jump(v))
- 2*dot(jump(u),average(Dh(v)*normal()))
- 2*dot(jump(v),average(Dh(u)*normal())), iopt);
lh = integrate (dot(f(),v), iopt)
+ integrate ("boundary", beta*penalty()*dot(g(),v)
- 2*dot(g(),Dh(v)*normal()), iopt);
b = integrate (dot(u,grad_h(q)), iopt)
+ integrate ("internal_sides", - dot(average(u),normal())*jump(q), iopt);
kh = integrate ("boundary", dot(g(),normal())*q, iopt);
c = integrate ("internal_sides", h_local()*jump(p)*jump(q), iopt);
mp = integrate (p*q, iopt);
}
g
u_exact g
Definition: burgers_diffusion_exact.h:33
form
see the form page for the full documentation
field
see the field page for the full documentation
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
mkgeo_ball.f
f
Definition: mkgeo_ball.sh:221
space
see the space page for the full documentation
mkgeo_ball.c
c
Definition: mkgeo_ball.sh:153
p
Definition: sphere.icc:25
rheolef::Dh
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type Dh(const Expr &expr)
Dh(uh): see the expression page for the full documentation.
Definition: field_expr_terminal.h:1010
rheolef::ddot
T ddot(const tensor_basic< T > &a, const tensor_basic< T > &b)
ddot(x,y): see the expression page for the full documentation
Definition: tensor.cc:278
a
Definition: diffusion_isotropic.h:25
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
stokes_dirichlet_dg
void stokes_dirichlet_dg(const space &Xh, const space &Qh, form &a, form &b, form &c, form &mp, field &lh, field &kh, integrate_option iopt=integrate_option())
Definition: stokes_dirichlet_dg.icc:25
test
see the test page for the full documentation
u
Definition: leveque.h:25
Float
see the Float page for the full documentation
mkgeo_ball.d
d
Definition: mkgeo_ball.sh:154
u
Float u(const point &x)
Definition: transmission_error.cc:26
mkgeo_ball.b
b
Definition: mkgeo_ball.sh:152
rheolef::penalty
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
Definition: field_expr_terminal.h:626
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
trial
see the test page for the full documentation
rheolef::details::dot
rheolef::details::is_vec dot
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60