Vector-valued manufactured solution used by the saddle-point program. More...

Inheritance diagram for Solution< dim, n_equations >:

Collaboration diagram for Solution< dim, n_equations >:

Public Member Functions
	Solution ()
	Construct a Solution with `n_equations` components.

virtual void	vector_value (const Point< dim > &p, Vector< double > &values) const override
	Evaluate the manufactured solution at a single point.

virtual void	vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, double > > &gradients) const override
	Evaluate the gradient of every component at a single point.

Detailed Description

template<int dim, int n_equations>
class Solution< dim, n_equations >

Vector-valued manufactured solution used by the saddle-point program.

The Solution class provides a closed-form expression for both components \((p,u)\) of the manufactured solution that the numerical scheme is supposed to recover. It is used in three different places inside the program:

as the Dirichlet boundary data inside SaddlePointProblem::setup_system (so that the discrete solution interpolates the manufactured values on \(\partial\Omega\)),
inside SaddlePointProblem::compute_error to evaluate the \(L^2\) and \(H^1\) errors of the numerical solution against the manufactured one, and
inside SaddlePointProblem::output_exact_results to write the manufactured solution to a .vtu file for visual comparison.

The currently active test case (test case 2) sets

first component: \(p(x,y) = e^{x}\cos y\),
second component: \(u(x,y) = -2xy\).

Test cases 1 and 3 (using sine functions) are present in the source but commented out; see the inline source.

Template Parameters

dim	Spatial dimension (assumed to be `2` in the manufactured expressions).
n_equations	Number of components in the vector solution (set to `2` from the outside).

Constructor & Destructor Documentation

◆ Solution()

template<int dim, int n_equations>

Solution< dim, n_equations >::Solution ( )

inline

Construct a Solution with n_equations components.

Forwards n_equations to the base-class constructor so that Function<dim>::n_components returns the correct value.

Member Function Documentation

◆ vector_gradient()

template<int dim, int n_equations>

void Solution< dim, n_equations >::vector_gradient	(	const Point< dim > &	p,
		std::vector< Tensor< 1, dim, double > > &	gradients
	)		const

overridevirtual

Evaluate the gradient of every component at a single point.

Writes one Tensor<1,dim> per component into gradients.

Parameters

[in]	p	Point at which the gradients are evaluated.
[out]	gradients	Vector that is first resized to `n_equations` and then filled with the gradient of each component.

◆ vector_value()

template<int dim, int n_equation>

void Solution< dim, n_equation >::vector_value	(	const Point< dim > &	p,
		Vector< double > &	values
	)		const

overridevirtual

Evaluate the manufactured solution at a single point.

Writes the vector value \((p(x,y), u(x,y))\) into values.