A New Error Analysis Of Nonconforming Bergan's Energy-orthogoonal Element For The Extended Fisher-Kolmogorov Equation

A non C0 nonconforming finite element method(FEM for short)is proposed and analyzed for the extended Fisher-Kolmogorov(EFK for short)equation by employing the Bergan's energy-orthogonal plate element.Because the shape function and its first derivatives of this element are discontinuous at the element's vertices,it is quite different from the conventional finite elements used in the existing literature.Thus a series of novel approaches including some a priori bounds,interpolation operator splitting and derivative transfer techniques are developed to prove the existence,uniqueness of finite element solutions and to derive optimal error estimates for both the semi-discrete and backward Euler fully-discrete schemes.At last,numerical experiments are also provided to verify the theoretical analysis.