Publications

Habilitation thesis

PhD thesis

Diploma thesis

Papers in edited journals

  1. S. Franz, S. Trostorff, M. Waurick:
    Numerical methods for changing type systems
    accepted for publication in IMAJNA, 2017 arXiv:1610.08824
  2. S. Franz, G. Matthies:
    A Unified Framework for Time-Dependent Singularly Perturbed Problems with Discontinuous Galerkin in Time
    accepted for publication in Math. Comp.
  3. S. Franz, K. Höhne, M. Waurick:
    A solution decomposition for a singularly perturbed 4th order problem
    Analysis, 37 (2017) 2, 77-100
  4. S. Franz, Chr. Xenophontos:
    On a connection between layer-adapted exponentially graded and S-type meshes
    accepted for publication in CMAM. arXiv:1611.07213
  5. S. Franz:
    Convergence of LPS-FEM for convection-diffusion problems on layer-adapted meshes
    BIT Numerical Mathematics. 57(3) (2017), 771-786
  6. S. Franz, K. Höhne, G. Matthies:
    Grad-Div stabilisation applied to inf-sup stable discretisations with S-type meshes for the Oseen problem
    IMA J. Numer. Anal., (2017)
  7. S. Franz:
    Analysis for a family of continuous-discontinuous Galerkin FEM for convection-diffusion problems.
    Appl. Numer. Math., 110 (2016), 93-109
  8. S. Franz, L. Ludwig, Chr. Xenophontos:
    Finite element approximation of convection-diffusion problems using an exponentially graded mesh
    Computer Math. Appl., 72 (2016) 6, 1532-1540
  9. S. Franz, H.-G. Roos:
    Robust error estimation in energy and balanced norms for singularly perturbed forth order problems
    Computer Math. Appl., 72 (2016) 1, 233-247
  10. S. Franz, H.-G. Roos:
    Error estimation in a balanced norm for a convection-diffusion problem with two different boundary layers.
    Calcolo, 51 (2014) 3, 423-440 , Addendum
  11. S. Franz, H.-G. Roos:
    Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems.
    Numer. Math. Theor. Meth. Appl., 7 (2014) 3, 356-373 , arXiv:1307.7543
  12. S. Franz, H.-G. Roos, A. Wachtel:
    A C0 interior penalty method for a singularly-perturbed fourth-order elliptic problem on a layer-adapted mesh.
    Numer. Methods Partial Differential Equations, 30 (2014) 3, 838-861
  13. S. Franz:
    Superconvergence Using Pointwise Interpolation in Convection-Diffusion Problems.
    Appl. Numer. Math., 76 (2014), 132-144 , arXiv:1304.7443
  14. S. Franz:
    Convergence Phenomena of Q_p-Elements for Convection-Diffusion Problems.
    Numer. Methods Partial Differential Equations, 29 (2013) 1, 280-296
  15. S. Franz, R. Gärtner, H.-G. Roos and A. Voigt:
    A Note on the Convergence Analysis of a Diffuse-Domain Approach.
    CMAM, 12 (2012) 2, 153-167
  16. S. Franz, R. B. Kellogg, M. Stynes:
    Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities.
    Mathematics of Computation, 81 (2012), 278, 661-685, preprint as pdf
  17. S. Franz, N. Kopteva:
    Green's function estimates for a singularly perturbed convection-diffusion problem.
    Journal of Differential Equations, 252 (2012), 1521-1545, preprint as pdf
  18. S. Franz, N. Kopteva:
    Green's function estimates for a singularly perturbed convection-diffusion problem in three dimensions.
    Int. J. Numer. Anal. Model. Ser. B, 2 (2011) 2-3, 124-141 , preprint as pdf
  19. S. Franz, G. Matthies:
    Convergence on Layer-adapted Meshes and Anisotropic Interpolation Error Estimates of Non-Standard Higher Order Finite Elements.
    Appl. Numer. Math., 61 (2011), 723-737 , corrected preprint
  20. S. Franz:
    SDFEM with non-standard higher-order finite elements for a convection-diffusion problem with characteristic boundary layers.
    BIT Numerical Mathematics, 51 (2011) 3, 631-651 , preprint
  21. S. Franz, H.-G. Roos:
    The Capriciousness of Numerical Methods for Singular Perturbations.
    SIAM Review, 53 (2011) 1, 157-173 , preprint
  22. S. Franz, G. Matthies:
    Local projection stabilisation on S-type meshes for convection-diffusion problems with characteristic layers.
    Computing, 87 (2010) 3-4, 135-167 , preprint
  23. S. Franz, T. Linß, H.-G. Roos, S. Schiller:
    Uniform superconvergence of a finite element method with edge stabilization for convection-diffusion problems.
    J. Comp. Math., 28 (2010) 1, 32-44 , preprint
  24. S. Franz, L. Tobiska, H. Zarin:
    A New Approach to Recovery of Discontinuous Galerkin.
    J. Comp. Math., 27 (2009) 6, 697-712 , preprint
  25. S. Franz, F. Liu, H.-G. Roos, M. Stynes, A. Zhou:
    The combination technique for a two-dimensional convection-diffusion problem with exponential layers.
    Appl. Math., 54 (2009) 3, 203-223 , preprint
  26. S. Franz, T. Linß, H.-G. Roos:
    Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers,
    Appl. Numer. Math., 58 (2008) 12, 1818-1829 , preprint
  27. S. Franz:
    Continuous interior penalty method on a Shishkin mesh for convection-diffusion problems with characteristic boundary layers,
    Comput. Meth. Appl. Mech. Engng., 197 (2008) 45-48, 3679-3686 , preprint
  28. S. Franz, T. Linß:
    Superconvergence analysis of the Galerkin FEM for a singularly perturbed convection-diffusion problem with characteristic layers,
    Numer. Methods Partial Differential Equations, 24 (2008) 1, 144-164 , preprint
  29. N.A. Adams, S. Hickel, S. Franz:
    Implicit subgrid-scale modeling by adaptive deconvolution,
    J. Comput. Phys. 200 (2004) 2, 412-431

Papers in Proceedings

  1. S. Franz, H.-G. Roos:
    On robust error estimation for singularly perturbed fourth-order problems
    In Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016
    Lecture Notes in Computational Science and Engineering 120 (2017), 77-85, Springer, Berlin Heidelberg,
  2. S. Franz, H.-G. Roos:
    Robust error estimation in energy and balanced norms for singularly perturbed forth order problems
    Model. Anal. Inform. Sist., 23:3 (2016), 364-369
  3. S. Franz, J. Rubisch:
    A discontinuous Galerkin method for fractional differential equations
    PAMM, 16 (2016), 761-762
  4. S. Franz, N. Kopteva:
    On the Sharpness of Green's function estimates for a convection-diffusion problem.
    In Proceedings of the Fifth Conference on Finite Difference Methods: Theory and Applications (FDM: T&A 2010), (2011), 44-57, Rousse University Press, arXiv:1102.4520v2
  5. S. Franz, R. B. Kellogg, M. Stynes:
    On the choice of mesh for a singularly perturbed problem with a corner singularity.
    In BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods
    Lecture Notes in Computational Science and Engineering 81 (2010), 119-126, Springer, Berlin Heidelberg, preprint as pdf
  6. S. Franz, G. Matthies:
    Local projection stabilisation on layer-adapted meshes for convection-diffusion problems with characteristic layers (Part I and II)
    In BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods
    Lecture Notes in Computational Science and Engineering 81 (2010), 127-138, Springer, Berlin Heidelberg, preprint as pdf
  7. S. Franz, T. Linß:
    Superconvergence analysis of Galerkin FEM and SDFEM for Elliptic Problems with characteristic layers,
    Proceedings in Applied Mathematics and Mechanics 6 (2006) 1, 737-738.
  8. N.A. Adams, S. Franz, S. Hickel, P. Koumoutsakos:
    Optimization of an implicit subgrid-scale model for LES,
    In Proceedings of the 21st International Congress of Theoretical and Applied Mechanics, Warsaw, Poland, 2004

Preprints and submitted papers

  1. S. Franz, M. Waurick:
    Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problems
    submitted. arXiv:1711.08640
  2. P. Constantinou, S. Franz, L. Ludwig, Chr. Xenophontos:
    A mixed hp FEM for the approximation of a 4th order singularly perturbed problem
    submitted.
  3. S. Franz, N. Kopteva:
    Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions.
    arXiv:1103.2948v2
  4. S. Franz:
    A recovery operator for the combination method.
    Preprint MATH-NM-09-2008, 10/2008, preprint as pdf

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Author: Sebastian Franz
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