QUASI-OPTIMAL ERROR ESTIMATES FOR THE FINITE ELEMENT APPROXIMATION OF STABLE HARMONIC MAPS WITH NODAL CONSTRAINTS

被引：0

作者：

Bartels, Soren ^{[1
]}

Palus, Christian ^{[1
]}

Wang, Zhangxian ^{[1
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Abt Angew Math, D-79104 Freiburg, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2023年 / 61卷 / 04期

关键词：

harmonic maps; finite elements; inverse function theorem; saddle-point formulation; error estimate; UNIQUENESS; STABILITY;

D O I：

10.1137/22M1524497

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation, we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal discretization of the unit-length constraint. The error analysis is based on an equivalent formulation of the constrained discrete problem as a mixed finite element scheme. The resulting estimate holds under natural regularity requirements and appropriate geometric stability conditions on solutions. Extensions to other target manifolds, including boundaries of ellipsoids, are discussed.

引用

页码：1819 / 1834

页数：16

共 39 条

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