Bivariate variational splines with monotonicity constraints

We present an approximation method of surfaces preserving the monotonicity constraints. By minimizing a semi-norm and monotonicity criteria we define the notion of the pseudo-monotone interpolating variational spline in a finite element space. We compute this spline by using a suitable algorithm. Some convergence results are carefully studied. Finally, to show the effectiveness of this method we give some numerical and graphical examples.