Superconvergence of an H-1-Galerkin nonconforming mixed finite element method for a parabolic equation

作者：Zhang Yadong; Shi Dongyang^*

来源：Computers & Mathematics with Applications, 2013, 66(11): 2362-2375.

DOI：10.1016/j.camwa.2013.09.013

• H-1-Galerkin mixed FEM
• Superconvergence
• Nonconforming FE
• Parabolic problem
• Semi-discrete and fully-discrete schemes

By choosing a suitable pair of approximating spaces, an H-1-Galerkin nonconforming mixed finite element method (FEM) is proposed for a class of parabolic equations under semi-discrete, backward Euler and Crank-Nicolson fully-discrete schemes, in which the famous EQ(1)(rot) element and zero order Raviart-Thomas element are used to approximate the primitive solution u and the flux (p) over right arrow = del u, respectively. Based on special characters of the elements considered, the corresponding optimal order error estimates for u in broken H-1-norm and (p) over right arrow in H(div)-norm are obtained for the above schemes. Furthermore, the global superconvergence results are derived through the postprocessing technique. The numerical results show the validity of the theoretical analysis.

• 出版日期2013-12
• 单位郑州大学; 许昌学院