Morley FEM for the fourth-order nonlinear reaction-diffusion problems

Nonconforming Morley finite element method is applied to a fourth order nonlinear reaction-diffusion problems. After deriving some regularity results to be used subsequently in our error analysis, Morley FEM is employed to discretize in the spatial direction to obtain a semidiscrete problem. A priori bounds for the discrete solution are derived and with the help of an auxiliary problem, optimal error estimates are proved for the semidiscrete scheme. Based on backward Euler method, a completely discrete scheme is analysed and wellposedness of the discrete problem is discussed. A priori error bounds are derived. It is observed that constants do not depend exponentially on the inverse of a small parameter appeared as the coefficient in the fourth order term and all the results are derived when the initial data are in H02. Finally, some computational experiments are conducted to confirm our theoretical findings.