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=====  =====
==== General Information ====

  * **Solver Fortran File:** ''Compute2DNodalGradient.F90''
  * **Solver Name:** ''ElmerIce_MeshAdapt2D(Compute2DNodalGradient)''
  * **Required Output Variable(s):** 
    * (1) ''g'' (dofs=2)
  * **Required Input Variable(s):** 
    * (1) ''v''
  * **Optional Output Variable(s):** None  
  * **Optional Input Variable(s):** None

==== General Description ====
This is a pseudo solver (i.e. it is not solving an equation). This solver compute the nodal 2D gradient vector <m>g_i={{\partial v}/{\partial x_i}}</m> of a variable //v//.

This is used for example by the mesh adaptation procedure to compute the hessian of //v// ([[mesh:meshadaptation|Mesh Adaptation]]). 

By default (//FE consistent average = Logical True//), this is done using a //L²//-projection on the FE mesh; If //FE consistent average = False//, at a given node the derivative is simply the average of the derivatives evaluated at the node in each elements sharing the node. 

==== SIF contents ====
<code>

Solver 2
  Equation = "Nodal Gradient"
  Variable = -dofs 2 "g"
  Procedure = "ElmerIce_MeshAdapt2D" "Compute2DNodalGradient"

  Optimize Bandwidth = False

  Variable Name = string "v"
  FE consistent average = Logical True
End

</code>


==== Example ====
Examples for anisotropic mesh adaptation can be found under ''[ELMER_TRUNK]/elmerice/Tests/MMG2D_Aniso1'' and ''[ELMER_TRUNK]/elmerice/Tests/MMG2D_Aniso2'', where the mesh size is adapted using 1 or 2 variables (i.e. combining metric informations), respectively.