Energy-stable finite element method for a class of nonlinear fourth-order parabolic equations

In this paper, an energy-stable finite element method with the Crank-Nicolson type of temporal discretization scheme is developed and analyzed for a class of nonlinear fourth-order parabolic equations (including the Swift-Hohenberg (SH) equation and the extended Fisher-Kolmogorov (EFK) equation). In addition to the energy stability properties, the optimal spatial convergence properties in both L infinity(L2)-and L infinity(H1)-norm and the second-order temporal approximation rate are also obtained for numerical solutions approximating to the real solution and its Laplacian for the developed energy-stable finite element method in both semi-and fully discrete schemes. Numerical experiments are carried out to validate all attained theoretical results.(c) 2023 Elsevier B.V. All rights reserved.