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mfem.gridfunction.normH1
Computes the H1 norm of a grid function.
Syntax
mfem.gridfunction.normH1(gf)
Description
Computes the H1 norm of a grid function. The H1 norm is defined as: ``` ||u||_H1 = sqrt( ||u||²_L2 + ||∇u||²_L2 ) = sqrt( ∫_Ω |u(x)|² dx + ∫_Ω |∇u(x)|² dx ) ``` This norm measures both the function values and their derivatives, making it suitable for error analysis in elliptic PDEs. **Note:** This function returns the H1 seminorm (gradient norm only). To get the full H1 norm, combine with the L2 norm: `sqrt(normL2(gf)**2 + normH1(gf)**2)`
Parameters
| Name | Description |
|---|---|
| gf | - GridFunction to compute norm of |
Returns
number