A Conforming Discontinuous Galerkin Finite Element Method For Solving Time-Dependent Brinkman Equation

In this paper,we use conforming discontinuous finite elements to solve the time-dependent Brinkman equation.The Conforming Discontinuous Galerkin(CDG)finite element method is an efficient numerical method for solving partial differential equations.The idea is to increase the degree of the weak differential operator to satisfy the weak continuity of the numerical solution.Compared with the Weak Galerkin finite element method,replacing the boundary function with the average of the internal function reduces the degree of freedom.Removing the stabilizer reduces the complexity of numerical com-putation.In this paper,the CDG method is used to solve the time-dependent Brinkman problem.Firstly,the definitions of Sobolev space and weak function space,discrete weak gradient,bilinear form are given.Secondly,the corresponding new variational forms are proposed in the case of semi-discrete space discreteness and total discreteness discretized for space time,respectively,the error equations under semi-discrete and fully discrete cases are established,and the error estimation under L~2norm and H~1norm is further given.Finally,some numerical examples are given to verify the accuracy and effectiveness of the method.