Sobolev方程的最小二乘混合有限元方法

Least-squares Mixed Finite Element Method for Sobolev Equation

本文提出了一种新的最小二乘混合有限元方法求解Sobolev方程。采用了对u和σ不同指标的有限元空间进行计算(LBB条件不需要),分析了此逼近格式的收敛性,并给出相应的误差估计。误差结果表明此种数值方法具有最优的收敛阶,并且关于时间具有二阶的收敛精度。

By introducing an unknown variable w = ut, a new least-squares mixed finite element procedure is formulated to solve the Sobolev equation. The convergence of approximate solution is analyzed under the standard regularity assumption on finite element partition （the LBB-condition is not required）. The optimal error estimate in L^2 × H^1-norm is derived. The error result also shows that this method yields the approximate solution with second-order accuracy in time increment.