Free Access
Issue
ESAIM: M2AN
Volume 54, Number 1, January-February 2020
Page(s) 229 - 253
DOI https://doi.org/10.1051/m2an/2019058
Published online 27 January 2020
  1. G. Acosta and J.P. Borthagaray, A fractional Laplace equation: regularity of solutions and finite element approximations. SIAM J. Numer. Anal. 55 (2017) 472–495. [Google Scholar]
  2. G. Acosta, F.M. Bersetche and J.P. Borthagaray, A short FE implementation for a 2D homogeneous Dirichlet problem of a fractional Laplacian. Comput. Math. Appl. 74 (2017) 784–816. [Google Scholar]
  3. G. Alzetta, D. Arndt, W. Bangerth, V. Boddu, B. Brands, D. Davydov, R. Gassmoeller, T. Heister, L. Heltai, K. Kormann, M. Kronbichler, M. Maier, J.-P. Pelteret, B. Turcksin and D. Wells, The deal.II library, version 9.0. J. Numer. Math. 26 (2018) 173–183. [CrossRef] [Google Scholar]
  4. P. Auscher, S. Hofmann, M. Lacey, A. McIntosh, P. Tchamitchian, The solution of the Kato square root problem for second order elliptic operators on ∝n. Ann. Math. 156 (2002) 633–654. [Google Scholar]
  5. S. Bartels, Numerical methods for nonlinear partial differential equations. In: Vol. 47 of Springer Series in Computational Mathematics. Springer, Cham (2015). [CrossRef] [Google Scholar]
  6. A. Bonito and J.E. Pasciak, Numerical approximation of fractional powers of elliptic operators. Math. Comp. 84 (2015) 2083–2110. [CrossRef] [Google Scholar]
  7. A. Bonito and J.E. Pasciak, Numerical approximation of fractional powers of regularly accretive operators. IMA J. Numer. Anal. 37 (2017) 1245–1273. [CrossRef] [Google Scholar]
  8. A. Bonito, J.P. Borthagaray, R.H. Nochetto, E. Otárola and A.J. Salgado, Numerical methods for fractional diffusion. Comput. Vis. Sci. 19 (2018) 19–46. [Google Scholar]
  9. A. Bonito, W. Lei and J.E. Pasciak, Numerical approximation of the integral fractional Laplacian. Numer. Math. 142 (2019) 235–278. [Google Scholar]
  10. A. Bonito, W. Lei and J.E. Pasciak, On sinc quadrature approximations of fractional powers of regularly accretive operators. J. Numer. Math. 27 (2017). [Google Scholar]
  11. J.P. Borthagaray, R.H. Nochetto and A.J. Salgado, , Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Preprint: arXiv:1806.08048 (2018). [Google Scholar]
  12. S.I. Boyarchenko and S.Z. Levendorski, Perpetual American options under Lévy processes. SIAM J. Control Optim. 40 (2002) 1663–1696. [Google Scholar]
  13. J.H. Bramble, J.E. Pasciak and P.S. Vassilevski, Computational scales of Sobolev norms with application to preconditioning. Math. Comp. 69 (2000) 463–480. [CrossRef] [Google Scholar]
  14. M. Broadie and J. Detemple, The valuation of American options on multiple assets. Math. Finance 7 (1997) 241–286. [CrossRef] [Google Scholar]
  15. O. Burkovska and M. Gunzburger, Regularity analyses and approximation of nonlocal variational equality and inequality problems. J. Math. Anal. Appl. 478 (2019) 1027–1048. [Google Scholar]
  16. S.N. Chandler-Wilde, D.P. Hewett and A. Moiola, Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples. Mathematika 61 (2015) 414–443. [CrossRef] [Google Scholar]
  17. Z. Chen and R.H. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems. Numer. Math. 84 (2000) 527–548. [Google Scholar]
  18. P.G. Ciarlet, The finite element method for elliptic problems. In: Vol. 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2002). [Google Scholar]
  19. M. Dauge, Regularity and Singularities in Polyhedral Domains. Available on: https://perso.univ-rennes1.fr/monique.dauge/publis/Talk_Karlsruhe08.pdf (2008). [Google Scholar]
  20. M. D’Elia and M. Gunzburger, The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator. Comput. Math. Appl. 66 (2013) 1245–1260. [Google Scholar]
  21. A. Ern and J.-L. Guermond, Theory and practice of finite elements. In: Vol. 159 of Applied Mathematical Sciences. Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  22. A. Friedman, Variational Principles and Free-boundary Problems, edited byR.E. Krieger, 2nd edition, Publishing Co., Inc, Malabar, FL, 1988. [Google Scholar]
  23. G. Grubb, Fractional Laplacians on domains, a development of Hörmander’s theory of μ-transmission pseudodifferential operators. Adv. Math. 268 (2015) 478–528. [CrossRef] [Google Scholar]
  24. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, In: Vol. 31 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2000). [Google Scholar]
  25. J. Lund and K.L. Bowers, Sinc Methods for Quadrature and Differential Equations, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1992) [CrossRef] [Google Scholar]
  26. A.-M. Matache, T. von Petersdorff and C. Schwab, Fast deterministic pricing of options on Lévy driven assets. ESAIM: M2AN 38 (2004) 37–71. [CrossRef] [EDP Sciences] [Google Scholar]
  27. R. Musina, A.I. Nazarov and K. Sreenadh, Variational inequalities for the fractional Laplacian. Potential Anal. 46 (2017) 485–498. [CrossRef] [Google Scholar]
  28. J.-F. Rodrigues, Obstacle problems in mathematical physics, 114, Notas de Matemática [Mathematical Notes]. In: Vol. 134 ofNorth-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam (1987). [Google Scholar]
  29. X. Ros-Oton and J. Serra, The extremal solution for the fractional Laplacian. Calc. Var. Part. Differ. Equ. 50 (2014) 723–750. [CrossRef] [Google Scholar]
  30. L. Schwartz, Théorie des distributions. Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris (1966). [Google Scholar]
  31. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [Google Scholar]
  32. R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators. Rev. Mat. Iberoam. 29 (2013) 1091–1126. [CrossRef] [Google Scholar]
  33. M.E. Taylor, Pseudodifferential operators, In: Vol. 34 of Princeton Mathematical Series Princeton University Press, Princeton, NJ (1981). [Google Scholar]
  34. M.I. Višik and G.I. Èskin, Elliptic Convolution Equations in a Bounded Region and their Applications. Vol. 22 Uspehi Mat. Nauk (1967) 15–76. [Google Scholar]
  35. V.S. Vladimirov, Methods of the theory of generalized functions, In: Vol. 6 of Analytical Methods and Special Functions. Taylor & Francis, London (2002). [Google Scholar]
  36. P. Wei, Numerical Approximation of time Dependent Fractional Diffusion with Drift: Applications to Surface Quasi-Geostrophic Dynamics and Electroconvection. Ph.D. thesis, A&M University, Texas (2019). [Google Scholar]
  37. J. Xu, Theory of Multilevel Methods. Ph.D. thesis, Cornell University, Ithaca, NY (1989). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you