论文标题
对Stokes方程有限元解的后验和先验误差估计
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations
论文作者
论文摘要
对于2D和3D域上的Stokes方程，明确的后验和先验误差估计是针对有限元解的新开发的。解决Stokes方程的无发散条件的困难通过利用扩展的HyperCircle方法以及Scott-Vogelius有限元方案来解决。由于误差估计中的所有术语都具有明确的值，因此通过进一步应用间隔算术和经过验证的计算算法，计算结果为近似误差提供了严格的估计。作为提议误差估计的应用，考虑了Stokes操作员的特征值问题，并获得了特征值的严格界限。通过求解凸和非凸3D域上的Stokes方程来证明所提出的误差估计的效率。
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is solved by utilizing the extended hypercircle method along with the Scott-Vogelius finite element scheme. Since all terms in the error estimation have explicit values, by further applying the interval arithmetic and verified computing algorithms, the computed results provide rigorous estimation for the approximation error. As an application of the proposed error estimation, the eigenvalue problem of the Stokes operator is considered and rigorous bounds for the eigenvalues are obtained. The efficiency of proposed error estimation is demonstrated by solving the Stokes equation on both convex and non-convex 3D domains.
