A POSTERIORI ERROR ESTIMATES FOR APPROXIMATE SOLUTIONS OF THE OBSTACLE PROBLEM FOR THE

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

The paper is concerned with a functional identity and estimates which are fulfilled for the measures of deviations from exact solutions of the obstacle problem for the

作者简介

D. Apushkinskaya

People’s Friendship University of Russia named after Patrice Lumumba

Email: apushkinskaya@gmail.com
Moscow, Russia

A. Novikova

People’s Friendship University of Russia named after Patrice Lumumba

Email: aanovikova01@gmail.com
Moscow, Russia

S. Repin

People’s Friendship University of Russia named after Patrice Lumumba; Saint Petersburg Department of Steklov Mathematical Institute of RAS

Email: rpnspb@gmail.com
Moscow, Russia

参考

  1. Lions, J.-L. Variational inequalities / J.-L. Lions, G. Stampacchia // Comm. Pure Appl. Math. — 1967. — V. 20. — P. 493-519.
  2. Petrosyan, A. Regularity of Free Boundaries in Obstacle-Type Problems / A. Petrosyan, H. Shagholian, N.N. Uraltseva. — Providence : American Mathematical Society, 2012. — 221 p.
  3. Choe, H.J. On the obstacle problem for quasilinear elliptic equations of р-Laplacian type / H.J. Choe, J.L. Lewis // SIAM J. Math. Anal. — 1991. — V. 22, № 3. — P. 623-638.
  4. Andersson J. Optimal regularity for the obstacle problem for the р-Laplacian / J. Andersson, E. Lindgren, H. Shahgholian // J. Differ. Equat. — 2015. — V. 259, № 6. — P. 2167-2179.
  5. Jouvet, G. Steady, shallow ice sheets as obstacle problems: well-posedness and finite element approximation / G. Jouvet, E. Bueler // SIAM J. Appl. Math. — 2012. — V. 72, № 4. — P. 1292-1314.
  6. Lewicka, M. The obstacle problem for the р-Laplacian via optimal stopping of tug-of-war games / M. Lewicka, J.J. Manfredi // Probab. Theory Related Fields. — 2017. — V. 167, № 1-2. — P. 349-378.
  7. On the porosity of free boundaries in degenerate variational inequalities / L. Karp, T. Kipelainen, A. Petrosyan, H. Shagholian // J. Differ. Equat. — 2000. — V. 164, № 1. — P. 110-117.
  8. Lee, K. Hausdorff measure and stability for the p-obstacle problem (2
  9. Rodrigues, J.F. Stability remarks to the obstacle problem for p-Laplacian type equations / J.F. Rodrigues // Calc. Var. Partial Differ. Equat. — 2005. — V. 23, № 1. — P. 51-65.
  10. Falk, R.S. Error estimates for approximation of a class of a variational inequalities / R.S. Falk // Math. Comp. — 1974. — V. 28. — P. 963-971.
  11. Chen, Z., Residual type a posteriori error estimates for elliptic obstacle problems / Z. Chen, R. Nochetto // Numer. Math. — 2000. — V. 84. — P. 527—548.
  12. Repin, S.I. Accuracy of Mathematical Models — Dimension Reduction, Homogenization, and Simplification / S.I. Repin, S.A. Sauter. — Zurich : European Mathematical Society, 2020. — 317 p.
  13. Repin, S.I. A posteriori error estimation for variational problems with uniformly convex functionals / S.I. Repin // Math. Comp. — 2000. — V. 69, № 230. — P. 481-500.
  14. Репин, С.И. Апостериорные тождества для мер отклонений от точных решений нелинейных краевых задач / С.И. Репин // Журн. вычислит. математики и мат. физики. — 2023. — Т. 63, № 6. — С. 896-919.
  15. Repin, S. Error identities for variational problems with obstacles / S. Repin, J. Valdman // ZAMM Z. Angew. Math. Mech. — 2018. — Bd. 98, № 4. — S. 635-658.
  16. Apushkinskaya D.E. Thin obstacle problem: estimates of the distance to the exact solution / D.E. Apushkinskaya, S.I. Repin // Interfaces Free Bound. — 2018. — V. 20, № 4. — P. 511-531.
  17. Apushkinskaya, D.E. and Repin, S.I., Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions, Comput. Math. Math. Phys., 2020, vol. 60, no. 11, pp. 1823-1838.
  18. Apushkinskaya, D. Functional a posteriori error estimates for the parabolic obstacle problem / D. Apushkinskaya, S. Repin // Comput. Methods Appl. Math. — 2022. — V. 22, № 2. — P. 259276.
  19. Sharp numerical inclusion of the best constant for embedding H01 (Q) < Lp(Q) on bounded convex domain / K. Tanaka, K. Sekine, M. Mizuguchi, S. Oishi // J. Comput. Appl. Math. — 2017. — V. 311 — P. 306-313.
  20. Rossi, J.D. Optimal regularity at the free boundary for the infinity obstacle problem / J.D. Rossi, E.V. Teixeira, J.V. Urbano // Interfaces Free Bound. — 2015. — V. 17, № 3. — P. 381-398.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2024