论文标题
可变的多标准时间分节式亚扩散方程的后验错误分析
A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations
论文作者
论文摘要
考虑了次扩散类型的初始有限价值问题。 the temporal component of the differential operator has the form $\sum_{i=1}^{\ell}q_i(t)\, D _t ^{α_i} u(x,t)$, where the $q_i$ are continuous functions, each $D _t ^{α_i}$ is a Caputo derivative, and the $α_i$ lie in $（0,1] $。此问题的最大/比较原则在弱假设下证明了。多项式Mittag-Leffler功能的新阳性结果。在$ l_2（ω）$和$ l_ \ f iffty（ω）$中获得了后验错误范围，该$ l_2（ω）$ $ lifty（ω）$ $ω$ω$ cum br^d d。 $ d \ in \ {1,2,3 \} $。基于该理论的自适应算法进行了广泛的测试，并显示出在算法生成的网格上产生准确的数值解决方案。
An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form $\sum_{i=1}^{\ell}q_i(t)\, D _t ^{α_i} u(x,t)$, where the $q_i$ are continuous functions, each $D _t ^{α_i}$ is a Caputo derivative, and the $α_i$ lie in $(0,1]$. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in $L_2(Ω)$ and $L_\infty(Ω)$, where the spatial domain $Ω$ lies in $\bR^d$ with $d\in\{1,2,3\}$. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm.
