Numerical approximation of variational problems with orthotropic growth

被引：0

作者：

Balci, Anna Kh ^{[1
,2
]}

Diening, Lars ^{[2
]}

Salgado, Abner J. ^{[3
]}

机构：

[1] Charles Univ Prague, Dept Math Anal, Sokolovska 49-83, Prague 8, Czech Republic

[2] Univ Bielefeld, Dept Math, Postfach 10 01 31, D-33501 Bielefeld, Germany

[3] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

NUMERISCHE MATHEMATIK | 2024年

关键词：

65N30; 35J60; 35J75; 35J70; 46E30; 46E35; EXISTENCE; REGULARITY; UNIQUENESS;

D O I：

10.1007/s00211-024-01432-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the numerical approximation of variational problems with orthotropic growth, that is those where the integrand depends strongly on the coordinate directions with possibly different growth in each direction. Under realistic regularity assumptions we derive optimal error estimates. These estimates depend on the existence of an orthotropically stable interpolation operator. Over certain meshes we construct an orthotropically stable interpolant that is also a projection. Numerical experiments illustrate and explore the limits of our theory.

引用

页数：29

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