Publications by Dietmar Gallistl (Last update: 11 Dec 2024)

• D. Gallistl and N. T. Tran:
  Minimal residual discretization of a class of fully nonlinear elliptic PDE, 2024. [bibtex] [arXiv]

• D. Gallistl and S. Tian:
  A posteriori error estimates for nonconforming discretizations of singularly perturbed biharmonic operators,
  SMAI J. Comput. Math., volume 10, pp.355–372, 2024. [bibtex] [doi] [arXiv]
• D. Gallistl, M. Hauck, Y. Liang and D. Peterseim:
  Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound,
  IMA J. Numer. Anal., 2024. (online) [bibtex] [doi] [arXiv]
• D. Gallistl and R. Maier:
  Localized implicit time stepping for the wave equation,
  SIAM J. Numer. Anal., volume 62, no.4, pp.1589–1608, 2024. [bibtex] [doi] [arXiv] [pdf]
• D. Gallistl and N. T. Tran:
  Stability and guaranteed error control of approximations to the Monge–Ampère equation,
  Numer. Math., volume 156, no.1, pp.107–131, 2024. [bibtex] [doi] [arXiv] [full_text]
• P. Freese, D. Gallistl, D. Peterseim and T. Sprekeler:
  Computational multiscale methods for nondivergence-form elliptic partial differential equations,
  Comput. Methods Appl. Math., volume 24, no.3, pp.649–672, 2024. [bibtex] [doi] [arXiv] [full_text]
• D. Gallistl and S. Tian:
  Continuous finite elements satisfying a strong discrete Miranda–Talenti identity,
  IMA J. Numer. Anal., 2024. (online) [bibtex] [doi] [arXiv] [full_text]
• D. Brown and D. Gallistl:
  Multiscale sub-grid correction method for time-harmonic high-frequency elastodynamics with wave number explicit bounds,
  Comput. Methods Appl. Math., volume 23, no.1, pp.65–82, 2023. [bibtex] [doi] [arXiv]
• D. Gallistl:
  Mixed methods and lower eigenvalue bounds,
  Math. Comp., volume 92, no.342, pp.1491–1509, 2023. [bibtex] [doi] [preprint]
• D. Gallistl and N. T. Tran:
  Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equation,
  Math. Comp., volume 92, no.342, pp.1467–1490, 2023. [bibtex] [doi] [arXiv]
• D. Gallistl and V. Olkhovskiy:
  Computational lower bounds of the Maxwell eigenvalues,
  SIAM J. Numer. Anal., volume 61, no.2, pp.539–561, 2023. [bibtex] [doi] [arXiv] [pdf]
• K. Liu, D. Gallistl, M. Schlottbom and J. J. W. van der Vegt:
  Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements,
  IMA J. Numer. Anal., volume 43, no.4, pp.2320–2351, 2023. [bibtex] [doi] [arXiv]
• T. Chaumont-Frelet, D. Gallistl, S. Nicaise and J. Tomezyk:
  Wavenumber explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers,
  Comm. Math. Sci., volume 20, no.1, pp.1–52, 2022. [bibtex] [doi] [HAL]
• D. Gallistl, T. Sprekeler and E. Süli:
  Mixed finite element approximation of periodic Hamilton–Jacobi–Bellman problems with application to numerical homogenization,
  Multiscale Model. Simul., volume 19, no.2, pp.1041–1065, 2021. [bibtex] [doi] [pdf]
• D. Gallistl:
  A posteriori error analysis of the inf-sup constant for the divergence,
  SIAM J. Numer. Anal., volume 59, no.1, pp.249–264, 2021. [bibtex] [doi] [pdf]
• J. Fischer, D. Gallistl and D. Peterseim:
  A priori error analysis of a numerical stochastic homogenization method,
  SIAM J. Numer. Anal., volume 59, no.2, pp.660–674, 2021. [bibtex] [doi] [arXiv] [pdf]
• D. Gallistl and M. Schedensack:
  Taylor–Hood discretization of the Reissner–Mindlin plate,
  SIAM J. Numer. Anal., volume 59, no.3, pp.1195–1217, 2021. [bibtex] [doi] [pdf]
• D. Gallistl and M. Schedensack:
  A robust discretization of the Reissner–Mindlin plate with arbitrary polynomial degree,
  J. Comput. Math., volume 38, pp.1–13, 2020. [bibtex] [doi] [full_text]
• D. Gallistl and D. Peterseim:
  Numerical stochastic homogenization by quasilocal effective diffusion tensors,
  Commun. Math. Sci., volume 17, no.3, pp.637–651, 2019. [bibtex] [doi] [arXiv]
• D. Gallistl:
  Rayleigh-Ritz approximation of the inf-sup constant for the divergence,
  Math. Comp., volume 88, no.315, pp.73–89, 2019. [bibtex] [doi] [preprint]
• D. Gallistl:
  Numerical approximation of planar oblique derivative problems in nondivergence form,
  Math. Comp., volume 88, no.317, pp.1091–1119, 2019. [bibtex] [doi] [preprint]
• C. Carstensen, D. Gallistl and J. Gedicke:
  Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM,
  Numer. Math., volume 142, no.2, pp.205–234, 2019. [bibtex] [doi] [full_text]
• D. Gallistl and E. Süli:
  Mixed finite element approximation of the Hamilton–Jacobi–Bellman equation with Cordes coefficients,
  SIAM J. Numer. Anal., volume 57, no.2, pp.592–614, 2019. [bibtex] [doi] [pdf]
• D. Gallistl, P. Henning and B. Verfürth:
  Numerical homogenization of H(curl)-problems,
  SIAM J. Numer. Anal., volume 56, no.3, pp.1570–1596, 2018. [bibtex] [doi] [pdf]
• C. Carstensen, D. Gallistl and Y. Huang:
  Saturation and reliable hierarchical a posteriori Morley finite element error control,
  J. Comput. Math., volume 36, no.6, pp.833–844, 2018. [bibtex] [doi] [full_text]
• D. Gallistl and D. Peterseim:
  Computation of quasilocal effective diffusion tensors and connections to the mathematical theory of homogenization,
  Multiscale Model. Simul., volume 15, no.4, pp.1530–1552, 2017. [bibtex] [doi] [pdf]
• D. Gallistl:
  Stable splitting of polyharmonic operators by generalized Stokes systems,
  Math. Comp., volume 86, no.308, pp.2555–2577, 2017. [bibtex] [doi]
• D. Gallistl:
  Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients,
  SIAM J. Numer. Anal., volume 55, no.2, pp.737–757, 2017. [bibtex] [doi] [pdf]
• D. Boffi, D. Gallistl, F. Gardini and L. Gastaldi:
  Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form,
  Math. Comp., volume 86, no.307, pp.2213–2237, 2017. [bibtex] [doi]
• D. Gallistl, P. Huber and D. Peterseim:
  On the stability of the Rayleigh-Ritz method for eigenvalues,
  Numer. Math., volume 137, no.2, pp.339–351, 2017. [bibtex] [doi] [full_text]
• C. Carstensen, D. Gallistl and J. Gedicke:
  Justification of the saturation assumption,
  Numer. Math., volume 134, no.1, pp.1–25, 2016. [bibtex] [doi]
• C. Carstensen, D. Gallistl and M. Schedensack:
  $L^2$ best-approximation of the elastic stress in the Arnold-Winther FEM,
  IMA J. Numer. Anal., volume 36, no.3, pp.1096–1119, 2016. [bibtex] [doi] [full_text]
• D. Gallistl and D. Peterseim:
  Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering,
  Comput. Methods Appl. Mech. Eng., volume 295, pp.1–17, 2015. [bibtex] [doi] [arXiv]
• D. Gallistl:
  Morley finite element method for the eigenvalues of the biharmonic operator,
  IMA J. Numer. Anal., volume 35, no.4, pp.1779–1811, 2015. [bibtex] [doi] [full_text]
• D. Gallistl:
  An optimal adaptive FEM for eigenvalue clusters,
  Numer. Math., volume 130, no.3, pp.467–496, 2015. [bibtex] [doi]
• C. Carstensen, D. Gallistl and M. Schedensack:
  Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems,
  Math. Comp., volume 84, no.293, pp.1061–1087, 2015. [bibtex] [doi]
• C. Carstensen, D. Gallistl and N. Nataraj:
  Comparison results of nonstandard $P_2$ finite element methods for the biharmonic problem,
  ESAIM Math. Model. Numer. Anal., volume 49, pp.977–990, 2015. [bibtex] [doi]
• C. Carstensen, D. Gallistl and J. Hu:
  A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes,
  Comput. Math. Appl., volume 68, no.12, pp.2167–2181, 2014. [bibtex] [doi]
• C. Carstensen, D. Gallistl, F. Hellwig and L. Weggler:
  Low-order dPG-FEM for an elliptic PDE,
  Comput. Math. Appl., volume 68, no.11, pp.1503–1512, 2014. [bibtex] [doi]
• D. Gallistl, M. Schedensack and R. P. Stevenson:
  A remark on newest vertex bisection in any space dimension,
  Comput. Methods Appl. Math., volume 14, no.3, pp.317–320, 2014. [bibtex] [doi] [pdf]
• C. Carstensen and D. Gallistl:
  Guaranteed lower eigenvalue bounds for the biharmonic equation,
  Numer. Math., volume 126, no.1, pp.33–51, 2014. [bibtex] [doi]
• D. Gallistl:
  Adaptive nonconforming finite element approximation of eigenvalue clusters,
  Comput. Methods Appl. Math., volume 14, no.4, pp.509–535, 2014. [bibtex] [doi] [pdf]
• C. Carstensen, D. Gallistl and M. Schedensack:
  Discrete reliability for Crouzeix–Raviart FEMs,
  SIAM J. Numer. Anal., volume 51, no.5, pp.2935–2955, 2013. [bibtex] [doi] [pdf]
• C. Carstensen, D. Gallistl and M. Schedensack:
  Quasi-optimal adaptive pseudostress approximation of the Stokes equations,
  SIAM J. Numer. Anal., volume 51, no.3, pp.1715–1734, 2013. [bibtex] [doi] [pdf]
• C. Carstensen, D. Gallistl and J. Hu:
  A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles,
  Numer. Math., volume 124, no.2, pp.309–335, 2013. [bibtex] [doi]

• D. Gallistl:
  A posteriori error analysis of the inf-sup constant for the divergence,
  In Oberwolfach Reports, volume 18, no.1, pp.117–118, 2021. [bibtex] [doi] [preprint]
• D. Gallistl:
  Adaptive discretization of HJB equations with Cordes coefficients,
  In Oberwolfach Reports, volume 18, no.2, pp.1657–1658, 2021. [bibtex] [doi] [preprint]
• D. Gallistl:
  Numerical stochastic homogenization by quasilocal effective diffusion tensors,
  In Oberwolfach Reports, volume 16, no.3, pp.2163–2165, 2019. [bibtex] [doi] [full_text]
• D. Gallistl:
  Computation of the inf-sup constant for the divergence,
  In PAMM Proc. Appl. Math. Mech., volume 18, pp.1–2 (not consecutively paged), 2018. [bibtex] [doi] [full_text]
• D. Gallistl:
  Rayleigh–Ritz approximation of the inf-sup constant for the divergence,
  In Oberwolfach Reports, volume 15, no.4, pp.2876–2878, 2018. [bibtex] [doi] [preprint]
• P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus and J. Storn:
  Towards adaptive discontinuous Petrov-Galerkin methods,
  In PAMM Proc. Appl. Math. Mech., volume 16, pp.741–744, 2016. [bibtex] [doi]
• D. Gallistl:
  On the discrete reliability for nonconforming finite element methods,
  In Oberwolfach Reports, volume 13, no.3, pp.2550–2551, 2016. [bibtex] [doi]
• D. Gallistl, D. Peterseim and C. Carstensen:
  Multiscale Petrov-Galerkin FEM for acoustic scattering,
  In PAMM Proc. Appl. Math. Mech., volume 16, pp.745–746, 2016. [bibtex] [doi]
• D. Gallistl:
  An adaptive FEM for linear elliptic equations in nondivergence form with Cordes coefficients,
  In Oberwolfach Reports, volume 13, no.3, pp.2448–2449, 2016. [bibtex] [doi]
• D. Gallistl:
  Multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering,
  In Oberwolfach Reports, volume 12, no.3, pp.2580–2581, 2015. [bibtex] [doi]
• D. Gallistl:
  An optimal adaptive FEM for eigenvalue clusters,
  In Oberwolfach Reports, volume 10, no.4, pp.3267–3270, 2013. [bibtex] [doi]
• D. Gallistl:
  Quasi optimal adaptive pseudostress approximation of the Stokes equations,
  In Oberwolfach Reports, volume 9, no.1, pp.497–499, 2012. [bibtex] [doi]

• D. Brown, D. Gallistl and D. Peterseim:
  Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations,
  Chapter in Meshfree Methods for Partial Differential Equations VII (M. Griebel, M. A. Schweitzer, eds.), Springer, volume 115, pp.85–115, 2017. [bibtex] [doi]
• C. Carstensen, D. Gallistl and B. Krämer:
  Numerical algorithms for the simulation of finite plasticity with microstructures,
  Chapter in Analysis and computation of microstructure in finite plasticity (S. Conti, K. Hackl, eds.), Springer, volume 78, pp.1–30, 2015. [bibtex] [doi]

• Dietmar Gallistl:
  Mixed finite element approximation of elliptic equations involving high-order derivatives, Habilitation thesis, Karlsruher Institut für Technologie, Fakultät für Mathematik, 2018. [bibtex]
• Dietmar Gallistl:
  Adaptive finite element computation of eigenvalues, Doctoral dissertation, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. [bibtex] [url] [doi]

• D. Gallistl:
  The adaptive finite element method, Snapshots of modern mathematics from Oberwolfach, volume 13, 2016. [bibtex] [doi] [full_text]