Description

SF_DISC1 Linear discontinuous shape function (P1).

[ VBASE, NLDOF, XLDOF, SFUN ] = SF_DISC1( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates discontinuous linear shape functions with with values defined by a constant and derivatives in the cell interior.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
i_eval      scalar:  1             Evaluate function values
                    >1             Evaluate values of derivatives
n_sdim      scalar: 1-3            Number of space dimensions
n_vert      scalar: 2-8            Number of vertices per cell
i_dof       scalar: 1-n_ldof       Local basis function to evaluate
xi          [n_sdim(+1)]           Local coordinates of evaluation point
aInvJac     [n,n_sdim(+1)*n_sdim]  Inverse of transformation Jacobian
vBase       [n]                    Preallocated output vector
                                                                                  .
Output      Value/[Size]           Description
-----------------------------------------------------------------------------------
vBase       [n]                    Evaluated function values
nLDof       [4]                    Number of local degrees of freedom on
                                   vertices, edges, faces, and cell interiors
xLDof       [n_sdim,n_ldof]        Local coordinates of local dofs
sfun        string                 Function name of called shape function

See also: sf_disc0

Code listing

% Check for evaluation on simplicies.
 if( n_vert==n_sdim+1 )
   f_simplex = 1;
 else
   f_simplex = 0;
 end


 nLDof = [0 0 0 n_sdim+1];
 if( f_simplex )
   xLDof = ones(n_sdim+1,1)/(n_sdim+1);
 else
   xLDof = zeros(n_sdim,1);
 end
 xLDof = repmat(xLDof,1,n_sdim+1);
 sfun  = 'sf_disc1';


 switch i_eval   % Evaluation type flag.

   case {1}   % Evaluation of function values.

     if ( f_simplex || i_dof<=n_sdim )

       vBase = xi(i_dof);

     else

       vBase = 1;
     end

   case {2,3,4}   % Evaluation of first order derivatives.

     if ( f_simplex || i_dof<=n_sdim )

       i_col = i_dof+(i_eval-2)*(n_sdim+f_simplex);

       vBase = aInvJac(:,i_col);

     else

       vBase = 0;
     end

   otherwise
     vBase = 0;

 end