Numerical Methods For A Finite-Strain Plate And Its Boundary Problem

In this paper,we try to use DG method to solve a finite-strain plate equation.Dif-ferent from traditional model,we consider the plate by adding the concept of 'thickness'and 'normal strain'.we will solve a boundary problem of this plate model.We will also discuss the error of our method,and use numerical experiments to prove it.This thesis consists of the following two parts.Firstly,we simplify the plate into a stick.By studying this simple case,we achieve a reasonable numerical format and analyze its energy norms,then we provide an error estimate.we present a(k+1)-th order of accuracy for the scheme with alternative fluxes,yet a(k+1)-th order for the conservative one,here k is the order of polynomials in the finite element space.Besides,we provide several numerical experiments for this system.Next,we go back to two-dimensional plate,designing a numerical algorithm with(?)k element by referring to what we do in one-dimensional case.Then we analyze its en-ergy norms.Different from one-dimensional case,in two-dimensional plate model,we have to face uxy,vxy these two mixed derivative terms while we only have the Dirichlet boundary condition for u and v.Here,we build a variable ? to take the place of those mixed derivative terms so that we can design numerical fluxes reasonably.The other problem is the loss of accuracy when dealing with ??x,??y.Due to the problem above,we can only get k-th order of accuracy for u and v in the scheme theoretically.Several numerical experiments for this are provided to prove the validity of our method and analysis.