Scholarlink

<p>In this paper, we derive a priori error estimates for variational inequalities of the first kind in an abstract framework. This is done by combining the first Strang Lemma and the Falk Theorem. The main application consists of the derivation of a priori error estimates for Galerkin methods, in which “variational crimes” may perturb the underlying variational inequality. Different types of perturbations are incorporated into the abstract framework and are discussed in various examples. For instance, the perturbation caused by an inexact quadrature is examined in detail for the Laplacian obstacle problem. For this problem, guaranteed rates for the approximation error resulting from the use of a higher-order finite element method are derived. In numerical experiments, the influence of the number of quadrature points on the approximation error and on the quadrature-related error itself is studied for several discretization methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Error estimates for perturbed variational inequalities of the first kind

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月6日

查看全文
  • Lothar Banz,
  • Miriam Schönauer,
  • Andreas Schröder

摘要

In this paper, we derive a priori error estimates for variational inequalities of the first kind in an abstract framework. This is done by combining the first Strang Lemma and the Falk Theorem. The main application consists of the derivation of a priori error estimates for Galerkin methods, in which “variational crimes” may perturb the underlying variational inequality. Different types of perturbations are incorporated into the abstract framework and are discussed in various examples. For instance, the perturbation caused by an inexact quadrature is examined in detail for the Laplacian obstacle problem. For this problem, guaranteed rates for the approximation error resulting from the use of a higher-order finite element method are derived. In numerical experiments, the influence of the number of quadrature points on the approximation error and on the quadrature-related error itself is studied for several discretization methods.