摘要
本文将连续时空有限元方法和降基方法相结合研究一类抛物方程.该类降基连续时空有限元方法既具有时空高精度的优势,又具有降基法减少自由度的优点.并给出一类抛物方程的降基离散形式,证明数值解的存在唯一性.通过给出输出函数,研究对偶问题,证明降基连续时空有限元解的后验误差估计.
The continuous space-time finite element method and reduced-basis method are combined to study the parabolic equation. The method discussed here not only has high order accuracy in both space and time directions, but also has the virtue of reducing the degree of freedom. The discrete form of reduced basis method was given, the existence and uniqueness of the numerical solution was proved. The proof of posterior error estimates was obtained by constructing the output function and dual problem.
出处
《应用数学》
CSCD
北大核心
2017年第3期706-714,共9页
Mathematica Applicata
基金
国家自然科学基金(11361035)
内蒙古自然科学基金(2017MS0107
2014BS0101)
内蒙古高等学校科学研究项目(NJZY14013)
关键词
抛物方程
连续时空有限元方法
降基方法
后验误差估计
Parabolic equation
Continuous space-time finite element method
Reduced-basis method
Posterior error estimates
