# 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 or a MultiMeshFunction
norm_type
see below for alternatives.
mesh
optional Mesh or a MultiMesh 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