Regularity analyses and approximation of nonlocal variational equality and inequality problems
Regularity analyses and approximation of nonlocal variational equality and inequality problems
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非局部变分等式和不等式问题的正则分析和逼近
DOI：
10.1016/j.jmaa.2019.05.064
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发表时间：
2019
影响因子：
1.3
通讯作者：
M. Gunzburger
中科院分区：
文献类型：
--
作者：
O. Burkovska;M. Gunzburger
我们考虑由非局部积分算子驱动的线性和障碍问题，其中非局部相互作用仅限于有限半径的球。这些类型的算子用于模拟反常扩散，并且对于积分核的特殊选择，可简化为有界域上的分数拉普拉斯算子。通过非局部向量微积分，我们将问题改写为弱形式，从而产生相应的非局部变分等式和不等式问题。我们证明了这两个问题的最佳正则性结果，包括解和拉格朗日乘子的更高正则性。基于正则性结果，我们分析了线性问题的有限元近似的收敛性，并通过数值结果说明了理论结果。
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These types of operators are used to model anomalous diffusion and, for a special choice of the integral kernels, reduce to the fractional Laplace operator on a bounded domain. By means of a nonlocal vector calculus we recast the problems in a weak form, leading to corresponding nonlocal variational equality and inequality problems. We prove optimal regularity results for both problems, including a higher regularity of the solution and the Lagrange multiplier. Based on the regularity results, we analyze the convergence of finite element approximations for a linear problem and illustrate the theoretical findings by numerical results.
积分分数拉普拉斯障碍问题的加权索博列夫正则性和逼近率
影响因子：
3.5
作者：
Borthagaray, Juan Pablo;Nochetto, Ricardo H.;Salgado, Abner J.
通讯作者：
Salgado, Abner J.
一类积分微分算子障碍问题的有限元近似
DOI：
10.1051/m2an/2019058
发表时间：
2020
期刊：
ESAIM: Mathematical Modelling and Numerical Analysis
影响因子：
--
作者：
Bonito, Andrea;Lei, Wenyu;Salgado, Abner J.
通讯作者：
Salgado, Abner J.