THE h × p FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEMS CONSTRAINED BY STOCHASTIC ELLIPTIC PDES

Hyung-C. Lee, Jangwoon Lee
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Abstract

This paper analyzes the h p version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the h p error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems. Numerical examples are used to confirm the theoretical results.
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随机椭圆偏微分方程约束下最优控制问题的h × p有限元方法
本文分析了随机输入椭圆型偏微分方程约束下最优控制问题的p型有限元法。主要结果是,随机偏微分方程控制问题的hp误差界导致相应的直接问题相对于p的指数收敛率。数值算例验证了理论结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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