As far as I know, for getting a unique solution to a PDE we should impose some boundary conditions to the PDE. "The number of required auxiliary conditions is determined by the highest order derivative in each independent variable. "
My questions are: In any numerical method, especially in finite element method, is it valid:
1-) to use more boundary conditions than the highest order derivative in each independent variable.
2-) to use less boundary conditions than the highest order derivative in each independent variable.
2-) In this article while the highest order derivative of a spatial variable is in third order authors used four boundary conditions for that variable.
I can increase the number of articles like this.