Asymptotic Expansion And Super Convergence Of A Kind Of Quasilinear Parabolic And Hyperbolic Equations Using Generalized Finite Element Method

In this dissertation, super convergence of second-order quasilinear parabolic and hyperbolic equations is analyzed, by using orthogonal series theory and generalized finite element method (GFEM), and complete results are achieved. It is authenticated that nonlinear one-order ordinary differential intial-value problems, quasilinear parabolic problems and quasilinear hyperbolic problems are solved by interpolation coefficient finite element method.This dissertation includes the following contents:1.The preliminaries of GFEM for asymptotic expansions of guasilinear equationsand super convergence are introduced.2.The results of super convergence and asymptotic expansions of the solution of second-order quasilinear parabolic equations using GFEM are calculated. The super convergence of interpolation coefficient finite element method is discussed, aiming at semidiscretization format and discretization format of one dimensional parabolic problem. Finally the two-grid algorithm and its error analysis are introduced.3.Super convergence of semidiscretization interpolation coefficients of guasilinear hyperbolic equations is discussed by using GFEM.