The Finite Volume Element Method For Parabolic Equation On BB Dual Subdivision

In this paper, we discuss the finite volume element method for parabolic equation on triangular meshes subdivisions and BB dual subdivision. The construction of finite volume element method deals with partitions and dual subdivsions of the domain. The popular methods of dual subdivision are barycenter subdivsions (BMB) and circumcenter subdivisions (CC). In addition, BB dual subdivisions (by connecting barycenters directly) are used too. As for parabolic equation, it had been established the results of the optimal L2 and Hl estimate errors based on BMB dual subdivisions . But the theoretical analysis of the schemes based on BB dual subdivison is not discussed.Firstly we describe the semi-discrete and fully-discrete schemes of finite volume element method for parabolic equation on BB dual subdivisions. Subsequently, we correct and perfect the results of I/2 error estimate of the finite volume element method for the second order elliptic equation on BB dual subdivision under h3 quasi-parallelogram condition; besides, we estimate the differences between a(it/, nu/J and a(uh,HhUh), (uh,TlhUh) and (uh,Hhuh) respectively under h2 quasi-parallelogram condition; futhermore, we obtain the optimal L2 and H1 error estimates for semi-discrete scheme and fully-discrete implicit Euler and Crank-Nicloson schemes. Finally, we compute a numerical experiment and prove the validity of the method.