A MESHFREE METHOD FOR A PDE-CONSTRAINED OPTIMIZATION PROBLEM

被引：0
|
作者：
Hoff, Daniel [1 ]
Wendland, Holger [2 ]
机构：
[1] Tech Univ Ilmenau, Inst Math, D-98694 Ilmenau, Germany
[2] Univ Bayreuth, Dept Math, Appl & Numer Anal, D-95440 Bayreuth, Germany
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2021年 / 59卷 / 04期
关键词：
PDE-constrained optimization; radial basis functions; meshfree methods; kernel-based approximation; error analysis; SCATTERED-DATA INTERPOLATION; DIVERGENCE-FREE; RADIAL BASIS;
D O I：
10.1137/20M1363510
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a system of weakly coupled, elliptic PDEs. These equations are then solved using kernel-based collocation. We derive an error analysis and give numerical examples.
引用
收藏
页码：1896 / 1917
页数：22
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