Norms#
Norms#
Module for calculating norms over a mesh. This module provides functions to calculate norms, including L2 and H1 semi-norm, over a given mesh.
- phasefieldx.norms.norm_H1(field, msh, dx=Measure('cell', subdomain_id='everywhere'))[source]#
Compute the H1 norm of a field over a given mesh.
- Parameters:
- fielddolfinx.Function
The field for the H1 norm calculation.
- mshdolfinx.Mesh
The mesh over which the H1 norm is computed.
- dxufl.Measure, optional
The measure for integration over the mesh. Default is ufl.dx.
- Returns:
- norm_H1float
The H1 norm of the field over the mesh.
Notes
The H1 norm is computed using the formula: norm_H1 = sqrt( ∫ |field|^2 dx + ∫ |∇(field)|^2 dx )
where ‘∇’ represents the gradient operator, and ‘dx’ represents the integration over the entire mesh.
- phasefieldx.norms.norm_L2(field, msh, dx=Measure('cell', subdomain_id='everywhere'))[source]#
Compute the L2 norm of a field over a given mesh.
- Parameters:
- fielddolfinx.Function
The field for the L2 norm calculation.
- mshdolfinx.Mesh
The mesh over which the L2 norm is computed.
- dxufl.Measure, optional
The measure for integration over the mesh. Default is ufl.dx.
- Returns:
- norm_L2float
The L2 norm of the field over the mesh.
Notes
The L2 norm is computed using the formula: norm_L2 = sqrt( ∫ |field|^2 dx )
where ‘dx’ represents the integration over the entire mesh.
- phasefieldx.norms.norm_LP(field, msh, p=2, dx=Measure('cell', subdomain_id='everywhere'))[source]#
Compute the Lp norm of a field over a given mesh.
- Parameters:
- fielddolfinx.Function
The field for the Lp norm calculation.
- mshdolfinx.Mesh
The mesh over which the Lp norm is computed.
- pfloat, optional
The exponent for the Lp norm calculation. Default is 2.
- dxufl.Measure, optional
The measure for integration over the mesh. Default is ufl.dx.
- Returns:
- norm_LPfloat
The Lp norm of the field over the mesh.
Notes
The Lp norm is computed using the formula: norm_LP = ( ∫ |field|^p dx )^(1/p)
where ‘dx’ represents the integration over the entire mesh.
- phasefieldx.norms.norm_semiH1(field, msh, dx=Measure('cell', subdomain_id='everywhere'))[source]#
Compute the H1 semi-norm of a field over a given mesh.
- Parameters:
- fielddolfinx.Function
The field for the H1 semi-norm calculation.
- mshdolfinx.Mesh
The mesh over which the H1 semi-norm is computed.
- dxufl.Measure, optional
The measure for integration over the mesh. Default is ufl.dx.
- Returns:
- norm_semiH1float
The H1 semi-norm of the field over the mesh.
Notes
The H1 semi-norm is computed using the formula: norm_semiH1 = sqrt( ∫ |∇(field)|^2 dx )
where ‘∇’ represents the gradient operator, and ‘dx’ represents the integration over the entire mesh.