A Posteriori Error Estimates of Finite Element Solutions of Parametrized Nonlinear Equations

Abstract : Nonlinear differential equations with parameters are called parametrized nonlinear equations. This paper studies a posteriori error estimates of finite element solutions of second order parametrized strongly nonlinear equations in divergence form on one-dimensional bounded intervals. In the previous paper by the authors, the finite element solutions are defined, and several a priori estimates are proved on regular branches and on branches around turning points. Using obtained a priori error estimates, we obtain several practical a posteriori error estimates which are asymptotically exact. Some numerical examples are given.... Parametrized nonlinear equations, Fredholm operators, Regular branches, Turning points, Finite element solutions, A priori and a posteriori error estimates.