norm

dolfin.fem.norms.norm(v, norm_type='L2', mesh=None)

Return the norm of a given vector or function.

Arguments

v

a Vector or a Function.

norm_type

see below for alternatives.

mesh

optional Mesh on which to compute the norm.

If the norm type is not specified, the standard \(L^2\) -norm is computed. Possible norm types include:

Vectors

Norm	Usage
\(l^2\)	norm(x, ‘l2’)	Default
\(l^1\)	norm(x, ‘l1’)
\(l^\infty\)	norm(x, ‘linf’)

Functions

Norm	Usage	Includes the \(L^2\) -term
\(L^2\)	norm(v, ‘L2’)	Yes
\(H^1\)	norm(v, ‘H1’)	Yes
\(H^1_0\)	norm(v, ‘H10’)	No
\(H\) (div)	norm(v, ‘Hdiv’)	Yes
\(H\) (div)	norm(v, ‘Hdiv0’)	No
\(H\) (curl)	norm(v, ‘Hcurl’)	Yes
\(H\) (curl)	norm(v, ‘Hcurl0’)	No

Examples of usage

v = Function(V)
x = v.vector()

print norm(x, 'linf')   # print the infinity norm of vector x

n = norm(v)             # compute L^2 norm of v
print norm(v, 'Hdiv')   # print H(div) norm of v
n = norm(v, 'H1', mesh) # compute H^1 norm of v on given mesh