Analysis And Application Of The Covolume Method For Some Kinds Of Equations

In this paper, finite volume element method(FVEM) are proposed and analyzed for nonlinear parabolic problems and nonlinear parabolic problems and a generalized difference methods in L2 H1 and L∞ error estimates .The Chapter one is the introduction.In Chapter two, we consider the finite volume element Methods for nonlinear parabolic problemsOptimal order error estimates in the H1, L2norms and W1,∞ almost optimal error estimates in L∞ are demonstrated. Moreover superconvergence in the error between the approximate solution and the generalized elliptic projection of the exact solution is also shown.In Chapter three, we consider the finite volume element Mstheods for nonlinear hyperbolic problemsOn the basic of the chapter three , Optimal order error estimates in the H1, L2norms and W1,∞ almost optimal error estimates in L∞ are also demonstrated. Moreover super-convergence in the error between the approximate solution and the generalized elliptic projection of the exact solution is also shown.In Chapter four, we consider the generalized difference methods in L2, H1 and L error estimates for elliptic equation, parabolic integration differential equation and parabolic equation.