论文标题
光谱递延校正方法的后验误差估计
A posteriori Error Estimation for the Spectral Deferred Correction Method
论文作者
论文摘要
光谱递延校正方法是用于求解普通微分方程的递延校正方法的变体。该方法的一个好处是使用低阶方案迭代地产生高阶近似值。在本文中，我们考虑基于伴随的后验分析，以估计解决方案兴趣的误差。该误差公式是通过首先开发出鼻递延校正方法的鼻等效元素方法来得出的。然后将误差公式分为各种术语，每个术语都表征了误差的不同组成部分。这些组件可用于确定更改方法参数以最佳改善错误的最佳策略。
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order approximation. In this paper we consider adjoint-based a posteriori analysis to estimate the error in a quantity of interest of the solution. This error formula is derived by first developing a nodally equivalent finite element method to the spectral deferred correction method. The error formula is then split into various terms, each of which characterizes a different component of the error. These components may be used to determine the optimal strategy for changing the method parameters to best improve the error.
