论文标题
关于在目标误差估计中产生的线性代数系统的有效数值解决方案
On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates
论文作者
论文摘要
我们处理线性偏微分方程（PDE）的数值解，重点是面向目标的误差估计值，包括相应代数系统的不准确解决方案引起的代数误差。面向目标的误差估计需要解决原始和双代数系统的解决方案。我们使用BI-CONJUGATE梯度方法同时解决两个系统，该方法允许控制两个系统的代数错误。我们开发了一个停止标准，该标准可以廉价评估并确保代数误差的估计小于离散误差的估计。使用此标准和一种自适应网状细化技术，我们为PDE的数值解提供了一种有效且可靠的方法，该方法通过几个数值实验证明了这一点。
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The goal-oriented error estimates require the solution of the primal as well as dual algebraic systems. We solve both systems simultaneously using the bi-conjugate gradient method which allows to control the algebraic errors of both systems. We develop a stopping criterion which is cheap to evaluate and guarantees that the estimation of the algebraic error is smaller than the estimation of the discretization error. Using this criterion and an adaptive mesh refinement technique, we obtain an efficient and robust method for the numerical solution of PDEs, which is demonstrated by several numerical experiments.
