A Mixed Variable Finite Element Method for the Efficient Solution of Nonlinear Diffusion and Potential Flow Equations

Abstract

A recently developed method ([1]) for the efficient solution of nonlinear partial differential equations of the form $\frac{\partial }{{\partial x}}\left( {a\frac{{\partial u}}{{1\partial y}}} \right) + \frac{\partial }{{\partial y}}\left( {a\frac{{\partial u}}{{2\partial y}}} \right) + f = o$, where a_i = a_i(x,y,u,u_x,u_y,∇u), is further discussed in this paper. The method has applications in many important practical problems.