Stabilizing Discontinuous Galerkin Method For Solving Parabolic Equations

The thesis proposes a stabilizact Discontinuous Galerkin method with penalty termsin Broken Sobolev space. The method content the numerical stability and also the localconservativeness.It adopts a Discontinuous Galerkin method with penalty terms to this thesis fromthe perspective of space. A priori error analysis is also given and the optimal degreeof convergence is also obtained. The thesis will discrete the above formulation by usingForward Euler method, Backward Euler method, and Crank-Nicolson method from theperspective of time. A priori error analysis is also given and the optimal degree of con-vergence is also obtained.It gives a specifc numerical example at the end of the thesis.Then an expected result is obtained by using Freefem++.