New estimates of mixed finite element method for fourth-order wave equation

作者：Shi, Dongyang^*; Wang, Lele; Liao, Xin

来源：Mathematical Methods in the Applied Sciences, 2017, 40(12): 4448-4461.

DOI：10.1002/mma.4316

• fourth-order wave equation
• MFEM
• semi-discrete and fully discrete schemes
• superconvergence

The conforming bilinear mixed finite element method is established for a fourth-order wave equation. By applying the interpolation and projection simultaneously, the superclose and superconvergence results of order O(h(2)) for the original variable u and intermediate variable p = -a(1)(X)Delta u in H-1-norm are achieved for the semi-discrete and fully discrete schemes, respectively (where a(1)(X) is the coefficient appeared in the equation). The distinct advantage of this method is that it can reduce the smoothness of solutions u, ut, and p compared with the existing literature for getting optimal estimates alone. At last, some numerical results are carried out to validate the theoretical analysis.

• 出版日期2017-8
• 单位郑州大学