I noticed that when specifying 2-D problem with NxNy nodes, the coefficient matrix for the linear system is NxN, with N=(Nx+2)(Ny+2). I would expect something like NxN with N=(Nx+2)*(Ny+2). I understand the two extra points are probably related by implementation of boundary conditions, but I don't quite understand why the coefficient matrix is as large as it is. Please let me know if I am missing out on something fundamental.
I noticed that when specifying 2-D problem with NxNy nodes, the coefficient matrix for the linear system is NxN, with N=(Nx+2)(Ny+2). I would expect something like NxN with N=(Nx+2)*(Ny+2). I understand the two extra points are probably related by implementation of boundary conditions, but I don't quite understand why the coefficient matrix is as large as it is. Please let me know if I am missing out on something fundamental.