Free Access
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S879 - S907
Published online 26 February 2021
  1. J.P. Agnelli, E.M. Garau and P. Morin, A posteriori error estimates for elliptic problems with dirac measure terms in weighted spaces. ESAIM: M2AN 48 (2014) 1557–1581. [CrossRef] [EDP Sciences] [Google Scholar]
  2. J. Alberty and S.A. Funken, Remarks around 50 lines of MATLAB: short finite element implementation. Numer. Algorithms 20 (1999) 117–137. [Google Scholar]
  3. T. Apel, A.-M. Sändig and J.R. Whiteman, Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains. Math. Methods Appl. Sci. 19 (1996) 63–85. [Google Scholar]
  4. T. Apel, O. Benedix, D. Sirch and B. Vexler, A priori mesh grading for an elliptic problem with Dirac right-hand side. SIAM J. Numer. Anal. 49 (2011) 992–1005. [Google Scholar]
  5. R. Araya, E. Behrens and R. Rodriguez, A posteriori error estimates for elliptic problems with Dirac delta source terms. Numer. Math. 196 (2007) 2800–2812. [Google Scholar]
  6. I. Babuska, Error-bounds for finite element method. Numer. Math. 16 (1971) 322–333. [Google Scholar]
  7. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, 3rd edition. In: Vol. 15 of Texts in Applied Mathematics. Springer, New York (2008). [CrossRef] [Google Scholar]
  8. E. Casas, L2 Estimates for the finite element method for the Dirichlet problem with singular data. Numer. Math. 47 (1985) 627–632. [Google Scholar]
  9. E. Cejas and R.G. Durán, Weighted a priori estimates for elliptic equations. Studia Math. 243 (2018) 13–24. [Google Scholar]
  10. C. D’Angelo, Finite element approximation of elliptic problems with Dirac measure terms in weighted spaces: applications to one- and three-dimensional coupled problems. SIAM J. Numer. Anal. 50 (2012) 194–215. [Google Scholar]
  11. I. Drelichman and R. Durán, Improved Poincaré inequalities with weights. J. Math. Anal. App. 347 (2008) 286–293. [Google Scholar]
  12. I. Drelichman, R. Durán and I. Ojea, A weighted setting for the Poisson problem with singular sources. SIAM J. Numer. Anal. 58 (2019) 590–60. [Google Scholar]
  13. J. Duoandikoetxea, Forty Years of Muckenhoupt Weights, Function Spaces and Inequalities. Charles University and Academy of Sciences, Prague (2013). [Google Scholar]
  14. R. Durán and F. López Garca, Solutions of the divergence and analysis of the Stokes equation in planar Hölder-α domains. Math. Models Methods. Appl. Sci. 20 (2010) 95–120. [Google Scholar]
  15. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, 2nd edition. In: Vol. 224 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Berlin-Heidelberg (1983). [Google Scholar]
  16. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Publishing Inc., Marshfield, MA (1985). [Google Scholar]
  17. J. Guzmán, D. Leykekhman, J. Rossmann and A.H. Schatz, Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods. Numer. Math. 112 (2009) 221–243. [Google Scholar]
  18. L.I. Hedberg, On certain convolution inequalities. Proc. Amer. Math. Soc. 36 (1972) 505–510. [Google Scholar]
  19. D. Jerison and C.E. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130 (1995) 161–219. [Google Scholar]
  20. T. Köppl and B. Wohlmuth, Optimal a priori error estimates for an eliptic problem with Dirac right-hand side. SIAM J. Num. An. 52 (2014) 1753–1769. [Google Scholar]
  21. H. Li, The Formula stability of the Ritz projection on graded meshes. Math. Comp. 86 (2017) 49–74. [Google Scholar]
  22. V.G. Maz’ya and J. Rossmann, Weighted Lp estimates of solutions to boundary value problems for second order elliptic systems in polyhedral domains. Z. Angew. Math. Mech. 83 (2003) 435–467. [Google Scholar]
  23. V.G. Maz’ya and J. Rossmann, Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2010). [Google Scholar]
  24. R. Nochetto, E. Otárona and A. Salgado, Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications. Numer. Math. 132 (2016) 85–130. [Google Scholar]
  25. E. Otárola and A. Salgado, The Poisson and Stokes problems on weighted spaces in Lipschitz domains and under singular forcing. J. Math. Anal. App. 471 (2018) 599. [Google Scholar]
  26. J.V. Pellegrotti, E. Cortés, M.D. Bordenave, M. Caldarola, M.P. Kreuzer, A.D. Sánchez, et al., Plasmonic photothermal fluorescence modulation for homogeneous biosensing. ACSSensors 1 (2016) 1351–1357. [Google Scholar]
  27. E. Sawyer and R.L. Wheeden, Weighted inequalities or fractional integrals on euclidean and homogeneous spaces. Am. J. Math. 114 (1992) 813–874. [Google Scholar]
  28. L.R. Scott, Finite element convergence for singular data. Numer. Math. 21 (1973) 317–327. [Google Scholar]
  29. H. Si, TetGen, a Delaunay-based quatily tetrahedral mesh generator. ACM Trans. Math. Softw. 41 (2015) 1–11. [Google Scholar]

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