Well-posedness and Numerical Analysis of Mixed Variational-hemivariational Inequalities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917241087328256 |
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| author | Han, Weimin Huang, Jianguo Yao, Yuan |
| author_facet | Han, Weimin Huang, Jianguo Yao, Yuan |
| contents | The paper is devoted to well-posedness analysis and the numerical solution of a family of general elliptic mixed variational-hemivariational inequalities. Various mixed variational equations, mixed variational inequalities and mixed hemivariational inequalities found in the literature are special cases of the mixed variational-hemivariational inequalities. Well-posedness of the mixed variational-hemivariational inequalities and their numerical approximations are studied via the projection iteration technique. Error analysis of the numerical methods is presented. The results are applied to the study of a variational-hemivariational inequality of the Stokes equations for incompressible fluid flows subject to slip conditions of frictional type, both monotone and non-monotone. Optimal order error estimates are derived for the use of some stable finite element space pairs under certain solution regularity assumptions. Numerical results are reported demonstrating the theoretical prediction of convergence orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01529 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness and Numerical Analysis of Mixed Variational-hemivariational Inequalities Han, Weimin Huang, Jianguo Yao, Yuan Numerical Analysis 65N30, 35J50, 49J40, 74M10, 74M15 The paper is devoted to well-posedness analysis and the numerical solution of a family of general elliptic mixed variational-hemivariational inequalities. Various mixed variational equations, mixed variational inequalities and mixed hemivariational inequalities found in the literature are special cases of the mixed variational-hemivariational inequalities. Well-posedness of the mixed variational-hemivariational inequalities and their numerical approximations are studied via the projection iteration technique. Error analysis of the numerical methods is presented. The results are applied to the study of a variational-hemivariational inequality of the Stokes equations for incompressible fluid flows subject to slip conditions of frictional type, both monotone and non-monotone. Optimal order error estimates are derived for the use of some stable finite element space pairs under certain solution regularity assumptions. Numerical results are reported demonstrating the theoretical prediction of convergence orders. |
| title | Well-posedness and Numerical Analysis of Mixed Variational-hemivariational Inequalities |
| topic | Numerical Analysis 65N30, 35J50, 49J40, 74M10, 74M15 |
| url | https://arxiv.org/abs/2602.01529 |