Open Access
Issue
ESAIM: M2AN
Volume 60, Number 4, July-August 2026
Page(s) 1549 - 1573
DOI https://doi.org/10.1051/m2an/2026038
Published online 08 July 2026
  1. S. Achatz, Higher order sparse grid methods for elliptic partial differential equations with variable coefficients. Computing 71 (2003) 1–15. [Google Scholar]
  2. V. Barthelmann, E. Novak and K. Ritter, High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 12 (2000) 273–288. [Google Scholar]
  3. Y. Bazilevs, L. Beirão Da Veiga, J.A. Cottrell, T.J.R. Hughes and G. Sangalli, Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes. Math. Models Methods Appl. Sci. 16 (2006) 1031–1090. [Google Scholar]
  4. J. Beck, G. Sangalli and L. Tamellini, A sparse-grid isogeometric solver. Comput. Methods Appl. Mech. Eng. 335 (2018) 128–151. [Google Scholar]
  5. L. Beiráo da Veiga, A. Buffa, J. Rivas and G. Sangalli, Some estimates for h–p–k-refinement in isogeometric analysis. Numer. Math. 118 (2011) 271–305. [Google Scholar]
  6. L. Beirão da Veiga, D. Cho and G. Sangalli, Anisotropic NURBS approximation in isogeometric analysis. Comput. Methods Appl. Mech. Eng. 209–212 (2012) 1–11. [Google Scholar]
  7. R.E. Bellman, Adaptive Control Processes: A Guided Tour. Princeton University Press, Princeton, NJ (1961). [Google Scholar]
  8. H.-J. Bungartz, Finite Elements of Higher Order on Sparse Grids. Berichte aus der Informatik, Shaker (1998). [Google Scholar]
  9. H.-J. Bungartz and T. Dornseifer, Sparse grids: Recent developments for elliptic partial differential equations. In: Multigrid Methods V, Springer, Berlin Heidelberg (1998) 45–70. [Google Scholar]
  10. H.-J. Bungartz and M. Griebel, Sparse grids. Acta Numer. 13 (2004) 147–269. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Ciarlet and P. Raviart, Interpolation theory over curved elements, with applications to finite element methods. Comput. Methods Appl. Mech. Eng. 1 (1972) 217–249. [Google Scholar]
  12. F. Deluzet, C. Guillet and J. Narski, A hierarchical sparse-grid particle method for the Vlasov–Poisson system. SIAM J. Numer. Anal. (Submitted) (2026). [Google Scholar]
  13. T. Dornseifer and C. Pflaum, Discretization of elliptic differential equations on curvilinear bounded domains with sparse grids. Computing 56 (1996) 197–213. [Google Scholar]
  14. D.R. Forsey and R.H. Bartels, Hierarchical B-spline refinement. SIGGRAPH Comput. Graph. 22 (1988) 205–212. https://doi.org/10.1145/378456.378512 [Google Scholar]
  15. J. Garcke, Sparse grids in a nutshell. Lect. Notes Comput. Sci. Eng. 88 (2013) 57–80. [Google Scholar]
  16. M. Griebel, The combination technique for the sparse grid solution of PDE’s on multiprocessor machines. Parallel Process. Lett. 02 (1992) 61–70. [CrossRef] [Google Scholar]
  17. M. Griebel, Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Computing 61 (1998) 151–179. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Griebel and J. Hamaekers, Sparse grids for the Schrödinger equation. ESAIM: M2AN 41 (2007) 215–247. [Google Scholar]
  19. M. Griebel and H. Harbrecht, A note on the construction of L-fold sparse tensor product spaces. Constr. Approx. 38 (2013) 235–251. [Google Scholar]
  20. M. Griebel and H. Harbrecht, On the construction of sparse tensor product spaces. Math. Comp. 82 (2013) 975–994. [Google Scholar]
  21. M. Griebel and H. Harbrecht, On the convergence of the combination technique. In Sparse Grids and Applications—Munich 2012, edited by Jochen Garcke. Springer International Publishing, Cham (2014) 55–74. [Google Scholar]
  22. M. Griebel, M. Schneider and C. Zenger, A combination technique for the solution of sparse grid problems, Forschungsberichte, TU Munich, TUM I, 9038 (1990) 1–24. [Google Scholar]
  23. T. Hughes, J. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194 (2005) 4135–4195. [CrossRef] [Google Scholar]
  24. C. Pflaum, Convergence of the combination technique for second-order elliptic differential equations. SIAM J. Numer. Anal. 34 (1997) 2431–2455. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Pflaum and A. Zhou, Error analysis of the combination technique. Numer. Math. 84 (1999) 327–350. [Google Scholar]
  26. E. Sande, C. Manni and H. Speleers, Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence. Math. Models Methods Appl. Sci. 29 (2019) 1175–1205. [Google Scholar]
  27. E. Sande, C. Manni and H. Speleers, Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis. Numer. Math. 144 (2020) 889–929. [Google Scholar]
  28. E. Sande, C. Manni and H. Speleers, Ritz-type projectors with boundary interpolation properties and explicit spline error estimates. Numer. Math. 151 (2022) 475–494. [Google Scholar]
  29. H. Speleers, Hierarchical spline spaces: quasi-interpolants and local approximation estimates. Adv. Comput. Math. 43 (2017) 235–255. [Google Scholar]
  30. H. Speleers and C. Manni, Effortless quasi-interpolation in hierarchical spaces. Numer. Math. 132 (2016) 155–184. [Google Scholar]
  31. S. Takacs, Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations. Math. Models Methods Appl. Sci. 28 (2018) 1899–1928. [Google Scholar]
  32. S. Takacs and T. Takacs, Approximation error estimates and inverse inequalities for B-splines of maximum smoothness. Math. Models Methods Appl. Sci. 26 (2016) 1411–1445. [Google Scholar]

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