Matania Ben-Artzi - Papers 2008-2024

  1. (with J. Falcovitz and J. Li) The convergence of the GRP scheme, Discrete and Continuous Dynamical Systems 23 (2009),1-27. (pdf)

  2. (with J.-P. Croisille and D. Fishelov) A fast direct solver for the biharmonic problem in a rectangular grid, SIAM J. Sci. Comput. 31 (2008), 303-333 . (pdf)

  3. (with J. Falcovitz) Generalized Riemann problems: From the scalar equation to multidimensional fluid dynamics, in "Recent Advances in Computational Sciences", pp. 1-50, World Scientific, 2008, Eds. P. Jorgensen, X. Shen, C-W. Shu, N. Yan. (pdf)

  4. Spectral theory for divergence-form operators, in "Spectral and Scattering Theory and Related Topics", Ed. H. Ito, RIMS Kokyuroku 1607 (2008), 77-84. (pdf)

  5. (with S. Benachour and P. Laurencot) Sharp decay estimates and vanishing viscosity for diffusive Hamilton-Jacobi equations, Adv. Diff. Eqs. 14 (2009), 1-25 . (pdf)

  6. (with J. Falcovitz and Ph. LeFloch) Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme, J. Comp. Phys. 228 (2009), 5650-5668 . (pdf)

  7. (with I. Chorev, J.-P. Croisille and D. Fishelov) A compact difference scheme for the biharmonic equation in planar irregular domains, SIAM J. Numer. Anal. 47 (2009), 3087-3108 . (pdf)

  8. (with J.-P. Croisille and D. Fishelov) A high order compact scheme for the pure streamfunction formulation of the Navier-Stokes equations, J. Sci. Comput. 42(2010) , 216-250. (pdf)

  9. (with M. Bank) Scalar conservation laws on a half-line: A parabolic approach, J. Hyperbolic Diff. Eqs. 7(2010), 165-189 . (pdf)

  10. Smooth Spectral Calculus, In: M. Demuth, B.-W. Schulze and I. Witt (Eds.): "Partial Differential Equations and Spectral Theory", pp. 119-182. ( Vol. 211 in the series "Operator Theory: Advances and Applications"). Springer Basel, 2010. (pdf)

  11. (with J.-P. Croisille and D. Fishelov) Recent developments in the pure streamfunction formulation of the Navier-Stokes equations, J. Sci. Comput. 45(2010), 238-258. (pdf)

  12. (with J.-P. Croisille and D. Fishelov) Highly accurate discretization of the Navier-Stokes equations in streamfunction formulation, in "Spectral and High Order Methods for Partial Differential Equations" (Eds. J.S.Hesthaven and E.M. Ronquist), Lecture Notes in Computational Science and Engineering, Vol. 76, Springer. ( 2011), pp. 189-197. (pdf)

  13. (with J.-P. Croisille and D. Fishelov) Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation, AIP Conf. Proc. 1479 (2012), 1101-1104; doi: 10.1063/1.4756339. (pdf)

  14. Eigenfunction expansions and spacetime estimates for generators in divergence-form, Reviews in Mathematical Physics 22 ( 2010), 1209-1240 . (pdf)

    Erratum: Reviews in Mathematical Physics 26, (2014). (pdf)

  15. Divergence-type operators: Spectral theory and spacetime estimates , In: M. Ruzhansky, M. Sugimoto and J. Wirth (Eds.): "Evolution Equations of Hyperbolic and Schrodinger Type", pp. 1-40. ( Vol. 301 in the series "Progress in Mathematics"). Birkhauser-Springer Basel, 2012. (pdf)

  16. (with J.-P. Croisille and D. Fishelov) Recent advances in the study of a fourth-order compact scheme for the one-dimensional biharmonic equation, J. Sci. Comput. 53 (2012), 55-79. (pdf)

  17. (with J.-P. Croisille and D. Fishelov) An embedded compact scheme for biharmonic problems in irregular domains , In: K. Georgiev, M. Todorov, I. Georgiev (Eds.) "Advanced Computing in Industrial Mathematics" , pp. 11--23, Springer , 2018. (pdf)

  18. (with J.-P. Croisille, D. Fishelov and R. Katzir) Discrete fourth-order Sturm-Liouville problems , IMA J. Numer. Anal. 38 (2018), 1485--1522. (pdf)

  19. (with G. Katriel) Spline functions , the biharmonic operator and approximate eigenvalues, Numer. Mathematik, 141 (2019), 839--879 (pdf)

  20. (with J.-P. Croisille and D. Fishelov) Time evolution of discrete fourth-order elliptic operators, Numer. Meth. PDE, 35 (2019), 1429--1457. (pdf)

  21. (with M.Ruzhansky and M.Sugimoto) Spectral identities and smoothing estimates for evolution operators, Adv. Diff. Eqs., 25 ( 2020), 627--650. arXiv:1807.11611 (pdf)

  22. (with T.Umeda) Spectral theory of first-order systems: from crystals to Dirac operators, Reviews Math. Phys., 33 ( 2021), 52 pages. https://doi.org/10.1142/S0129055X21500148 (pdf)

  23. (with J. Li) Consistency of finite volume approximations to nonlinear hyperbolic balance laws , Math.Comp., 90 ( 2021), 141--169. (pdf)

  24. The Nash inequality in general domains with application to the linear Stokes system, Pure and Applied Func. Anal. ,5 (2020), 287--294. (pdf)

  25. (with M.Bank and M. Schonbek) Viscous conservation laws in 1D with measure initial data , Quart.Appl.Math.79 (2021), 103--124. http://arxiv.org/abs/1907.02807 (pdf)

  26. (with J.-P. Croisille and D. Fishelov) A Cartesian compact scheme for the Navier-Stokes equations in streamfunction formulation in irregular domains, J. Sci. Comp. 81 ( 2019), 1386--1408. (pdf)

  27. (with B. Kramer) Finite difference approach to fourth-order linear boundary-volume problems , IMA J. Numer. Anal. 41 (2021), 2530--2561. http://arxiv.org/abs/2004.01433 (pdf)

  28. (with J. Li) Regularity of fluxes in nonlinear hyperbolic balance laws, Communications Appl. Math. Computation 5 (2022), 1289--1298.
    DOI 10.1007/s42967-022-00224-y (pdf)

  29. (with J.-P. Croisille and D. Fishelov) Convergence of finite difference schemes: matrix versus kernel analysis , ``Lecture Notes in Computational Science and Engineering'' 137 (2022), 155--169. J. M. Melenk et al. (eds.), Springer.
    https://doi.org/10.1007/978-3-031-20432-6_8.

  30. (with A. Benabdallah and Y. Dermenjian) Concentration and non-concentration of eigenfunctions of second-order elliptic operators in layered media, J. Spect. Th. 13 (2023), 1173--1224. arXiv:2212.05872 (pdf)


  31. (with Y.Nachshon, H. Cohen and A. Maril) A model of similarity: Metric in a patch,
    (Preprint 2022) psyarxiv.com/fyd4q/ (pdf)

  32. (with J. Li) Hyperbolic conservation laws, integral balance laws and regularity of fluxes, Communications Appl. Math. Computation 6 (2023), 2048--2063.
    (pdf)


  33. (with Y.Eidelman and D. Fishelov)Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations, Numer. Algorithms 98 (2025), 625--649.
    https://doi.org/10.1007/s11075-024-01809-9 (pdf)


  34. GRP-a direct Godunov extension, J. Comput. Phys. 519 (2024), 113388.
    (pdf)


  35. Role of fluxes in high-order Godunov schemes, Communications in Comp. Phys. (to appear, 2025).