Local Discontinuous Galerkin Method For Solving Biot Equation

In this thesis,we discuss the Local discontinuous Galerkin(LDG)method based on al-ternating flux for solving two-dimensional Biot equation with periodic boundary con-ditions.We provide the stability analysis and the error estimates both for semidiscrete and full discrete scheme,in which the third order total variation diminishing explicit Runge-Kutta(TVDRK3)method is used for time discretization.When we consider the scheme,we should choose appropriate numerical flux.We repeatedly use the an-tisymmetry of DG spatial discretization to obtain stability with a simple and practical initial value setting.we can get the optimal L2 error estimate for each variable by using Gauss-Radau(GGR)projection technique and discrete version of Poincare's inequali-ty.And it's defining constant has nothing to do with permeability parameters.Several numerical examples have verified the effectiveness of the algorithm:LDG not only has high-order accuracy,but also can effectively overcome the locking phenomenon of numerical solutions.