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PreprintCC BY 4.0arXiv

A posteriori error estimates for variational inequalities of the second kind in an abstract framework

  • Lothar Banz
  • Miriam Schönauer
  • Andreas Schröder
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Abstract

In this paper, an abstract framework is introduced for the derivation of reliable a posteriori error estimators for variational inequalities of the second kind. Under certain conditions (local) efficiency of the error estimators can also be derived. The framework is based on the estimation of a residuum which results from an equivalent mixed formulation and from the replacement of the Lagrange multiplier by its (possibly post-processed) discrete counterpart. The approach is applied to an idealized frictional contact problem and a Mosolov type model problem in an hp-finite element discretization setup. Several numerical experiments demonstrate the broad applicability of the theoretical findings.

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Cite

BibTeXRIS
BibTeX
@misc{banz2026posteriori,
  title = {{A posteriori error estimates for variational inequalities of the second kind in an abstract framework}},
  author = {Lothar Banz and Miriam Schönauer and Andreas Schröder},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26001},
  eprint = {2609.26001},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26001},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A posteriori error estimates for variational inequalities of the second kind in an abstract framework
AU  - Lothar Banz
AU  - Miriam Schönauer
AU  - Andreas Schröder
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26001
UR  - https://arxiv.org/abs/2609.26001
AB  - In this paper, an abstract framework is introduced for the derivation of reliable a posteriori error estimators for variational inequalities of the second kind. Under certain conditions (local) efficiency of the error estimators can also be derived. The framework is based on the estimation of a residuum which results from an equivalent mixed formulation and from the replacement of the Lagrange multiplier by its (possibly post-processed) discrete counterpart. The approach is applied to an idealized frictional contact problem and a Mosolov type model problem in an hp-finite element discretization setup. Several numerical experiments demonstrate the broad applicability of the theoretical findings.
ER  -