Divergence-free quasi-interpolation

Applied and Computational Harmonic Analysis - Tập 60 - Trang 471-488 - 2022
Wenwu Gao1,2,3, Gregory E. Fasshauer3, Nicholas Fisher4
1School of Big Data and Statistics, Anhui University, Hefei, PR China
2Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, PR China
3Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80401, USA
4Department of Mathematics and Statistics, Minnesota State University, Mankato, MN 56001, USA

Tài liệu tham khảo

Alfeld, 2016, Linear differential operators on bivariate spline spaces and spline vector fields, BIT Numer. Math., 56, 15, 10.1007/s10543-015-0557-x Amodei, 1994, A vector spline quasi-interpolation, 1 Atteia, 1993, Quasi-interpolant elastic manifolds, UNAM, 3 Beatson, 1992, Univariate multiquadric approximation: quasi-interpolation to scattered data, Constr. Approx., 8, 275, 10.1007/BF01279020 Benbourhim, 1997, Generalized variational quasi-interpolants in (Hm(Ω))n, Bol. Soc. Mat. Mexicana, 3 Benbourhim, 2010, Meshless pseudo-polyharmonic divergence-free and curl-free vector fields approximation, SIAM J. Numer. Anal., 42, 1218, 10.1137/080743743 Buhmann, 1988, Convergence of univariate quasi-interpolation using multiquadrics, IMA J. Numer. Anal., 8, 365, 10.1093/imanum/8.3.365 Buhmann, 1993, On quasi-interpolation with radial basis functions, J. Approx. Theory, 72, 103, 10.1006/jath.1993.1009 Buhmann, 1995, On quasi-interpolation by radial basis functions with scattered centres, Constr. Approx., 11, 239, 10.1007/BF01203417 Chen, 1999, Div-curl vector quasi-interpolation on a finite domain, Math. Comput. Model., 30, 179, 10.1016/S0895-7177(99)00124-7 Cheney, 1992, On kernels and approximation orders, vol. 138, 227 Chui, 1987, A natural formulation of quasi-interpolation by multivariate splines, Proc. Am. Math. Soc., 99, 643, 10.1090/S0002-9939-1987-0877032-6 Chui, 1990, A characterization of multivariate quasi-interpolation formulas and its applications, Numer. Math., 57, 105, 10.1007/BF01386401 Chui, 1987, A multivariate analog of Marsden's identity and a quasi-interpolation scheme, Constr. Approx., 3, 111, 10.1007/BF01890557 Cucker, 2001, On the mathematical foundations of learning, Bull. Am. Math. Soc., 39, 1, 10.1090/S0273-0979-01-00923-5 Cucker, 2007, Learning Theory: An Approximation Theory Viewpoint, 10.1017/CBO9780511618796 Dodu, 2004, Irrotational or divergence-free interpolation, Numer. Math., 98, 477, 10.1007/s00211-004-0541-x Dyn, 1992, On multivariate approximation by integer translates of a basis function, Isr. J. Math., 78, 95, 10.1007/BF02801574 Fuselier, 2008, Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants, Math. Comput., 77, 1407, 10.1090/S0025-5718-07-02096-0 Fuselier, 2009, Error and stability estimates for surface-divergence free RBF interpolants on the sphere, Math. Comput., 78, 2157, 10.1090/S0025-5718-09-02214-5 Gao, 2017, Constructing radial kernels with higher-order moment conditions, Adv. Comput. Math., 43, 1355, 10.1007/s10444-017-9528-x Gao, 2020, Optimality and regularization properties of quasi-interpolation: deterministic and stochastic approaches, SIAM J. Numer. Anal., 58, 2059, 10.1137/19M1266496 Gao, 2020, Multivariate Monte Carlo approximation based on scattered data, SIAM J. Sci. Comput., 42, A2262, 10.1137/19M1249138 Grohs, 2013, Quasi-interpolation in Riemannian manifolds, IMA J. Numer. Anal., 33, 849, 10.1093/imanum/drs026 Grohs, 2017, Scattered manifold-valued data approximation, Numer. Math., 135, 987, 10.1007/s00211-016-0823-0 Guo, 2012, An empirical feature-based learning algorithm producing sparse approximations, Appl. Comput. Harmon. Anal., 32, 389, 10.1016/j.acha.2011.07.005 Guzman, 2018, Inf-sup stable finite-elements on barycentric refinements producing divergence-free approximation in arbitrary dimensions, SIAM J. Numer. Anal., 56, 2826, 10.1137/17M1153467 Jia, 1993, A new version of Strang–Fix conditions, J. Approx. Theory, 74, 221, 10.1006/jath.1993.1062 Lei, 1997, Approximation from shift-invariant spaces by integral operators, SIAM J. Math. Anal., 28, 481, 10.1137/S0036141095279869 Keim, 2016, A high-order, analytically divergence-free approximation method for the time-dependent Stokes problem, SIAM J. Numer. Anal., 54, 1288, 10.1137/151006196 Lanzara, 2007, Approximate approximations from scattered data, J. Approx. Theory, 145, 141, 10.1016/j.jat.2006.08.003 Lanzara, 2014, Approximation of solutions to multidimensional parabolic equations by approximate approximations, Appl. Comput. Harmon. Anal., 36, 167, 10.1016/j.acha.2013.06.003 Lanzara, 2016, Fast cubature of volume potentials over rectangular domains by approximate approximations, Appl. Comput. Harmon. Anal., 41, 749, 10.1016/j.acha.2015.06.001 Mu, 2018, A discrete divergence free weak Galerkin finite element method for the Stokes equations, Appl. Numer. Math., 125, 172, 10.1016/j.apnum.2017.11.006 Narcowich, 1994, Generalized Hermite interpolation via matrix-valued conditionally positive definite functions, Math. Comput., 63, 661, 10.1090/S0025-5718-1994-1254147-6 Narcowich, 2007, Divergence-free RBFs on surfaces, J. Fourier Anal. Appl., 13, 643, 10.1007/s00041-006-6903-2 Neilan, 2021, Divergence-free Scott-Vogelius elements on curved domains, SIAM J. Numer. Anal., 59, 1090, 10.1137/20M1360098 Rabut, 1991, An introduction to Schoenberg's approximation, Comput. Math. Appl., 24, 139 Rabut, 1991, How to build quasi-interpolants: applications to polyharmonic B-splines, 391 Rabut, 1992, Elementary m-harmonic cardinal B-splines, Numer. Algorithms, 2, 39, 10.1007/BF02142205 Rabut, 1992, High level m-harmonic cardinal B-splines, Numer. Algorithms, 2, 63, 10.1007/BF02142206 Schaback, 1997, Construction techniques for highly accurate quasi-interpolation operators, J. Approx. Theory, 91, 320, 10.1006/jath.1996.3101 Schoenberg, 1946, Contributions to the problem of approximation of equidistant data by analytic functions, Q. Appl. Math., 4, 45, 10.1090/qam/15914 Schräder, 2011, A high-order, analytically divergence-free discretization method for Darcy's problem, Math. Comput., 80, 263, 10.1090/S0025-5718-2010-02388-9 Smale, 2005, Shannon sampling II: connections to learning theory, Appl. Comput. Harmon. Anal., 19, 285, 10.1016/j.acha.2005.03.001 Stein, 1971 Sorokina, 2018, Bernstein-Bezier techniques for divergence of polynomial spline vector fields in Rn, Adv. Comput. Math., 44, 227, 10.1007/s10444-017-9541-0 Strang, 1973, A Fourier analysis of the finite-element method, 793 Sun, 2009, A note on application of integral operator in learning theory, Appl. Comput. Harmon. Anal., 26, 416, 10.1016/j.acha.2008.10.002 Vennell, 2009, A divergence-free spatial interpolator for large sparse velocity data sets, J. Geophys. Res., 114, 10, 10.1029/2008JC004973 Wendland, 2009, Divergence-free kernel methods for approximating the Stokes problem, SIAM J. Numer. Anal., 47, 3158, 10.1137/080730299 Wu, 1994, Shape preserving properties and convergence of univariate multiquadric quasi-interpolation, Acta Math. Appl. Sin., 10, 441, 10.1007/BF02016334 Wu, 2005, Generalized Strang–Fix condition for scattered data quasi-interpolation, Adv. Comput. Math., 23, 201, 10.1007/s10444-004-1832-6 Xu, 2010, A new divergence-free interpolation operator with applications to the Darcy-Stokes Brinkman equations, SIAM J. Sci. Comput., 32, 855, 10.1137/090751049 Ye, 2021, A numerical scheme with divergence free H-div triangular finite element for the Stokes equations, Appl. Numer. Math., 167, 211, 10.1016/j.apnum.2021.05.005