Finite Element Approximations Applied to the Nonlinear Boundary Value Problem $Δu = bu^2$

Summary In this paper, we consider finite element approximations for the nonlinear boundary value problem Au=buz, based on piecewise linear polynomials, and discuss iterative methods associated with the finite element schemes. Error estimates are obtained, which imply that the approximate solutions converge uniformly to the exact solution. Finally, we give some numerical examples indicating the effectiveness of our results. become more widely recognized and they are applied not only to linear boundary value problems, but also to nonlinear boundary value problems. In this paper, we study the application of the finite element schemes to the nonlinear boundary value problem of the form Au = bu2 in Q,