Lagrange

class dolfin.cpp.function.Lagrange(*args)

Bases: dolfin.cpp.common.Variable

Lagrange polynomial (basis) with given degree q determined by n = q + 1 nodal points. Example: q = 1 (n = 2) Lagrange p(1); p.set(0, 0.0); p.set(1, 1.0); It is the callers responsibility that the points are distinct. This creates a Lagrange polynomial (actually two Lagrange polynomials): p(0,x) = 1 - x (one at x = 0, zero at x = 1) p(1,x) = x (zero at x = 0, one at x = 1)

Copy constructor.

Parameters:Lagrange & p (const) –

ddx()

Return derivate of polynomial i at given point x

Parameters:

• i (std::size_t) – (std::size_t)
• x (double) – (double)

Return type:

double

degree()

Return degree

Return type:std::size_t Returns:std::size_t

dqdx()

Return derivative q (a constant) of polynomial

Parameters:i (std::size_t) – (std::size_t) Return type:double

eval()

Return value of polynomial i at given point x

Parameters:

• i (std::size_t) – (std::size_t)
• x (double) – (double)

Return type:

double

point()

Return point

Parameters:i (std::size_t) – (std::size_t) Return type:double

set()

Specify point

Parameters:

• i (std::size_t) – (std::size_t)
• x (double) – (double)

Return type:

void

size()

Return number of points

Return type:std::size_t Returns:std::size_t

thisown

The membership flag