mkAdapt - Specify criteria for grid refinement

Calling sequence:

mkAdapt(ErrCrit,unknown_list,old_unknown_list,params_list,`2DP1_gsq_bsf`);

Parameters:

ErrCrit - A function in accordance with which grid refinement is performed.

unknown_list - The list of unknowns as discussed above.

old_unknown_list - The list of unknowns at the previous timestep, as discussed above.

params_list - A list of scalar input parameters.

bsf_file - A file containing a Maple description of a particular finite element.

Synopsis:

• Generates code for evaluation of ErrCrit for each element of a grid ( currently implemented only for 2D meshes).
• ErrCrit must be a sum of the function ElementInt() and ElEdgeInt().

  ElementInt(expr)
  Description is given in mkFem

  ElEdgeInt(expr)
  It is designed to evaluate normal derivatives over an element's edges. Expr must be written as follows

   /  d        \        /  d        \ 
   |---- f(x,y)| nx  +  |---- f(x,y)| ny 
   \ dx        /        \ dy        / 
  

  where nx and ny denote x- and y-components of the normal vector, respectively. ElEdgeInt gives approximation to the Laplacian of f(x,y)

• An element is decided to be split, merged or left unchanged depending on the value of ErrCrit and parameters adaptHmin (smallest allowed element's size) and adaptTol (threshold for grid refinement).

Examples:

> # variation of phase-field variable and concentration field

> ErrCrit := ElEdgeInt(  diff(ph(x,y),x)*nx + diff(ph(x,y),y)*ny ) 
           + 100*ElementInt( ph(x,y)^2*(1-ph(x,y))**2 )
           + ElEdgeInt( diff(c(x,y),x)*nx+ diff(c(x,y),y)*ny):

> mkAdapt(ErrCrit,unknown_list,old_unknown_list,params_list,`2DP1_gsq_bsf`);

errfunk.f