large intervals, algorithm, convergence, evolution equations, nonlinear Galerkin method, Initial value problems for linear higher-order PDEs, stability, Article, Higher-order parabolic equations, 510.mathematics, finite elements, approximation of the attractor, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, hierarchial bases