非稳态奇异系数微分方程的时间间断时空有限元方法

TIME DISCONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR UNSTEADY DIFFERENTIAL EQUATION WITH SINGULAR COEFFICIENTS

针对一类二维单轴奇异系数非稳态问题构造了一种时间间断时空有限元格式,利用以Radau点为节点的Lagrange插值多项式的特性,结合有限差分法和有限元法的技巧证明了格式的稳定性和有限元解的时间最大模、空间加权L^2(Ω)-模误差估计.最后列举了一些数值试验结果,验证了理论结果和格式的可行性.

A time discontinuous space-time finite element formulation is presented for a class of twodimensional unsteady uniaxial problem with singular coefficients.By using the characteristic of Lagrange polynomial at Radau nodes,and the technique of combining finite difference method and finite element method,the stability of the scheme and the temporal maximum norm and spatial weighted L2(Ω)-norm error estimation of the finite element solution are proved.Finally,some numerical results are gieven to verify the theoretical results and the feasibility of the scheme.