Publications

Publications in Refereed Journals and Conference Proceedings
Preprints submitted for publication

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Preprints submitted for publication

  • Goal-oriented error estimation and adaptivity for stochastic collocation FEM (with Dirk Praetorius, Thomas Round, and Andrey Savinov).
    Preprint, arXiv: 2406.05028, 2024.
    Preprint on arXiv
  • Convergence analysis of the adaptive stochastic collocation finite element method (with Andrey Savinov).
    Preprint, arXiv: 2401.14894, 2024.
    Preprint on arXiv
  • Goal-oriented adaptive multilevel stochastic Galerkin FEM (with Dirk Praetorius and Michele Ruggeri).
    Preprint, arXiv:2208.09388, 2022.
    Preprint on arXiv
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Publications in Refereed Journals

  • Error estimation and adaptivity for stochastic collocation finite elements. Part II: multilevel approximation (with D. Silvester).
    SIAM Journal on Scientific Computing, Vol. 45 (2023), Issue 2, pp. A781-A797.
    Link to the paper      Preprint on arXiv
  • Error estimation and adaptivity for stochastic collocation finite elements. Part I: single-level approximation (with D. Silvester and F. Xu).
    SIAM Journal on Scientific Computing, Vol. 44 (2022), Issue 5, pp. A3393-A3412.
    Link to the paper      Preprint on arXiv
  • Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM (with D. Praetorius and M. Ruggeri).
    IMA Journal of Numerical Analysis, Vol. 42 (2022), Issue 3, pp. 2190-2213.
    Link to the paper      Preprint
  • Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM (with D. Praetorius and M. Ruggeri).
    SIAM/ASA Journal on Uncertainty Quantification, Vol. 9 (2021), Issue 3, pp. 1184-1216.
    Link to the paper      Preprint on arXiv
  • Truncation preconditioners for stochastic Galerkin finite element discretizations (with D. Loghin and R. Youngnoi).
    SIAM Journal on Scientific Computing, Vol. 43 (2021), Issue 5, pp. S92-S116.
    Link to the paper      Preprint on arXiv
  • Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations (with A. Khan, C. E. Powell and D. J. Silvester).
    Mathematics of Computation, Vol. 90 (2021), Issue 328, pp. 613-636.
    Link to the paper      Preprint on arXiv
  • T-IFISS: a toolbox for adaptive FEM computation (with L. Rocchi and D. Silvester).
    Computers & Mathematics with Applications, Vol. 81 (2021), pp. 373-390.
    Link to the paper      Preprint on arXiv
  • A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case (with F. Xu).
    Computers & Mathematics with Applications, Vol. 80 (2020), Issue 5, pp. 1084-1103.
    Link to the paper      Preprint on arXiv
  • Convergence of adaptive stochastic Galerkin FEM (with D. Praetorius, L. Rocchi and M. Ruggeri).
    SIAM Journal on Numerical Analysis, Vol. 57 (2019), no. 5, pp. 2359-2382.
    Link to the paper      Download pdf-file      Extended preprint on arXiv
  • Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation (with A. J. Crowder and C. E. Powell).
    SIAM Journal on Scientific Computing, Vol. 41 (2019), no. 3, pp. A1681-A1705.
    Link to the paper      Download pdf-file
  • Adaptive BEM with optimal convergence rates for the Helmholtz equation (with T. Betcke, A. Haberl and D. Praetorius).
    Computer Methods in Applied Mechanics and Engineering, Vol. 346 (2019), pp. 260-287.
    Link to the paper      Preprint on arXiv
  • Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs (with D. Praetorius, L. Rocchi and M. Ruggeri).
    Computer Methods in Applied Mechanics and Engineering, Vol. 345 (2019), pp. 951-982.
    Link to the paper      Preprint on arXiv
  • Efficient adaptive algorithms for elliptic PDEs with random data (with L. Rocchi).
    SIAM/ASA Journal on Uncertainty Quantification, Vol. 6 (2018), no. 1, pp. 243-272.
    Link to the paper      Download pdf-file
  • Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems (with A. Haberl and D. Praetorius).
    Computer Methods in Applied Mechanics and Engineering, Vol. 317 (2017), pp. 318-340.
    Link to the paper      Preprint on arXiv
  • Efficient adaptive stochastic Galerkin methods for parametric operator equations (with D. Silvester).
    SIAM Journal on Scientific Computing, Vol. 38 (2016), no. 4, pp. A2118-A2140.
    Link to the paper      Download pdf-file
  • A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces (with S. Nicaise).
    Computers & Mathematics with Applications, Vol. 71 (2016), no. 8, pp. 1636-1644.
    Link to the paper      Download the preprint (PDF)
  • The BEM with graded meshes for the electric field integral equation on polyhedral surfaces (with S. Nicaise).
    Numerische Mathematik, Vol. 132 (2016), no. 4, pp. 631-655.
    Link to the paper      Preprint on arXiv
  • Energy norm a posteriori error estimation for parametric operator equations (with C. E. Powell and D. Silvester).
    SIAM Journal on Scientific Computing, Vol. 36 (2014), no. 2, pp. A339-A363.
    Link to the paper (free access)     
  • A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data (with C. E. Powell and D. Silvester).
    SIAM Journal on Numerical Analysis, Vol. 50 (2012), no. 4, pp. 2039-2063.
    Link to the paper      Download from MIMS Eprints
  • A framework for the development of implicit solvers for incompressible flow problems (with D. Silvester and C. Powell).
    Discrete and Continuous Dynamical Systems - Series S, Vol. 5 (2012), no. 6, pp. 1195-1221.
    Link to the paper (free access)
  • Natural hp-BEM for the electric field integral equation with singular solutions (with N. Heuer).
    Numerical Methods for Partial Differential Equations, Vol. 28 (2012), Issue 5, pp. 1466-1480.
    Link to the paper
  • A new H(div)-conforming p-interpolation operator in two dimensions (with N. Heuer).
    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 45 (2011), no. 2, pp. 255-275.
    Link to the paper
  • Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces (with N. Heuer and R. Hiptmair).
    SIAM Journal on Numerical Analysis, Vol. 48 (2010), no. 4, pp. 1518-1529.
    Link to the paper
  • Natural p-BEM for the electric field integral equation on screens (with N. Heuer).
    IMA Journal of Numerical Analysis, Vol. 30 (2010), no. 3, pp. 595-628.
    Link to the paper
  • The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis (with N. Heuer).
    Applied Numerical Mathematics, Vol. 60 (2010), Issue 7, pp. 705-718.
    Link to the paper
  • The hp-version of the boundary element method with quasi-uniform meshes for weakly singular operators on surfaces (with N. Heuer).
    IMA Journal of Numerical Analysis, Vol. 30 (2010), no. 2, pp. 377-400.
    Link to the paper
  • Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions (with N. Heuer).
    SIAM Journal on Numerical Analysis, Vol. 47 (2009), Issue 5, pp. 3977-3989.
    Link to the paper
  • A note on the polynomial approximation of vertex singularities in boundary element methods in three dimensions.
    Journal of Integral Equations and Applications, Vol. 21 (2009), no. 3, pp. 359-380.
    Link to the paper
  • The hp-version of the boundary element method with quasi-uniform meshes in three dimensions (with N. Heuer).
    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 42 (2008), no. 5, pp. 821-849.
    Link to the paper
  • The hp-version of the BEM with quasi-uniform meshes for a three-dimensional crack problem: the case of a smooth crack having smooth boundary curve.
    Numerical Methods for Partial Differential Equations, Vol. 24 (2008), no. 4, pp. 1159-1180.
    Link to the paper
  • The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces (with N. Heuer).
    Numerische Mathematik, Vol. 106 (2007), no. 1, pp. 69-97.
    Link to the paper
  • On the finite element method for elliptic problems with degenerate and singular coefficients (with D. Arroyo and N. Heuer).
    Mathematics of Computation, Vol. 76 (2007), no. 258, pp. 509-537.
    Link to the paper
  • The p-version of the boundary element method for a three-dimensional crack problem (with N. Heuer).
    Journal of Integral Equations and Applications, Vol. 17 (2005), no. 3, pp. 243-258.
    Link to the paper
  • The p-version of the boundary element method for hypersingular operators on piecewise plane open surfaces (with N. Heuer).
    Numerische Mathematik, Vol. 100 (2005), no. 2, pp. 185-209.
    Link to the paper
  • Orthogonal systems of singular functions and numerical treatment of problems with degeneration of data.
    Advances in Computational Mathematics, Vol. 19 (2003), nos. 1-3, pp. 159-182.
    Link to the paper
  • The use of singular functions in the h-p version of the finite element method for the Dirichlet problem with degeneration of input data (with V. A. Rukavishnikov).
    Siberian Journal of Numerical Mathematics, Vol. 4 (2001), no. 3, pp. 201-228.
  • The exponential rate of convergence of the finite element method for the Dirichlet problem with singularity of the solution (with V. A. Rukavishnikov).
    Dokl. Russ. Acad. Nauk, Vol. 374 (2000), no. 6, pp. 727-731.
    English translation in: Russian Acad. Sci. Doklady Mathematics, Vol. 62 (2000), no. 2, pp. 266-270.
  • On the h-p version of the finite element method for one-dimensional boundary value problem with singularity of a solution (with V. A. Rukavishnikov).
    Siberian Journal of Numerical Mathematics, Vol. 1 (1998), no. 2, pp. 153-170.
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Publications in Refereed Conference Proceedings

  • High-order boundary element method for electromagnetic scattering at non-smooth surfaces (with N. Heuer).
    "Proceedings of the 10-th International Conference on the Mathematical and Numerical Aspects of Waves; Vancouver, Canada, July 25-29, 2011", ed. by N. Nigam, Pacific Institute for the Mathematical Sciences, Canada, 2011, pp. 121-124.
  • The p-version of the boundary element method for mixed boundary value problems on polyhedra (with N. Heuer).
    "Advances in Boundary Integral Methods, Proceedings of the 5th UK Conference on Boundary Integral Methods", ed. by K. Chen, University of Liverpool, UK, 2005, pp. 145-152.
  • Optimal a priori error estimate for the p-version of the BEM on open surfaces (with N. Heuer).
    "Proceedings of the International Conference on Computational Mathematics, ICCM-2004. Part II", ed. by G. A. Mikhailov, V. P. Il'in, and Y. M. Laevsky, ICM&MG Publishers, Novosibirsk, Russia, 2004, pp. 794-799.
  • An exponential rate of convergence of the finite element method for the Dirichlet problem with singularity of a solution (with V. A. Rukavishnikov).
    "ENUMATH-99. Proceedings of the Third European Conference on Numerical Mathematics and Advanced Applications, Jyvaskyla, Finland, July 26-30, 1999", ed. by P. Neittaanmaki, T. Tiihonen and P. Tarvainen, World Scientific, Singapore, 2000, pp. 681-689.
  • On the h-p version of the finite element method using singular functions (with V. A. Rukavishnikov).
    "The Far-Eastern School-Seminar on Mathematical Modeling and Numerical Analysis. The Proceedings &Abstracts", ed. by V. A. Rukavishnikov, Khabarovsk, 1999, pp. 6-13.