Publications
Preprints submitted for publication

A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case
(with F. Xu).
Preprint, arXiv:1903.06520 [math.NA], 2019.
Link to the preprint

Convergence of adaptive stochastic Galerkin FEM
(with D. Praetorius, L. Rocchi and M. Ruggeri).
Preprint, arXiv:1811.09462 [math.NA], 2018.
Link to the preprint

Robust a posteriori error estimation for stochastic Galerkin formulations of parameterdependent linear elasticity equations
(with A. Khan, C. E. Powell and D. J. Silvester).
Preprint, arXiv:1810.07440 [math.NA], 2018.
Link to the preprint
to the top
Publications in Refereed Journals

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, 2019 (to appear).
Link to the preprint

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. 260287.
Link to the paper
Preprint on arXiv

Goaloriented 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. 951982.
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. 243272.
Link to the paper
Download pdffile

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. 318340.
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. A2118A2140.
Link to the paper
Download pdffile

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. 16361644.
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. 631655.
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. A339A363.
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. 20392063.
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. 11951221.
Link to the paper (free access)

Natural hpBEM for the electric field integral equation with singular
solutions (with N. Heuer).
Numerical Methods for Partial Differential Equations,
Vol. 28 (2012), Issue 5, pp. 14661480.
Link to the paper

A new H(div)conforming pinterpolation operator in two dimensions
(with N. Heuer).
ESAIM: Mathematical Modelling and Numerical Analysis,
Vol. 45 (2011), no. 2, pp. 255275.
Link to the paper

Convergence of the natural hpBEM 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. 15181529.
Link to the paper

Natural pBEM for the electric field integral equation on screens
(with N. Heuer).
IMA Journal of Numerical Analysis,
Vol. 30 (2010), no. 3, pp. 595628.
Link to the paper

The hpBEM with quasiuniform 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. 705718.
Link to the paper

The hpversion of the boundary element method with quasiuniform
meshes for weakly singular operators on surfaces (with N. Heuer).
IMA Journal of Numerical Analysis,
Vol. 30 (2010), no. 2, pp. 377400.
Link to the paper

Optimal error estimation for H(curl)conforming pinterpolation
in two dimensions (with N. Heuer).
SIAM Journal on Numerical Analysis,
Vol. 47 (2009), Issue 5, pp. 39773989.
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. 359380.
Link to the paper

The hpversion of the boundary element method with quasiuniform
meshes in three dimensions (with N. Heuer).
ESAIM: Mathematical Modelling and Numerical Analysis,
Vol. 42 (2008), no. 5, pp. 821849.
Link to the paper

The hpversion of the BEM with quasiuniform meshes for a
threedimensional crack problem: the case of a smooth crack having smooth
boundary curve.
Numerical Methods for Partial Differential Equations,
Vol. 24 (2008), no. 4, pp. 11591180.
Link to the paper

The pversion 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. 6997.
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. 509537.
Link to the paper

The pversion of the boundary element method for a threedimensional
crack problem (with N. Heuer).
Journal of Integral Equations and Applications,
Vol. 17 (2005), no. 3, pp. 243258.
Link to the paper

The pversion of the boundary element method for hypersingular operators
on piecewise plane open surfaces (with N. Heuer).
Numerische Mathematik, Vol. 100 (2005), no. 2, pp. 185209.
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. 13, pp. 159182.
Link to the paper

The use of singular functions in the hp 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. 201228.

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. 727731.
English translation in: Russian Acad. Sci. Doklady Mathematics, Vol. 62
(2000), no. 2, pp. 266270.

On the hp version of the finite element method for onedimensional
boundary value problem with singularity of a solution
(with V. A. Rukavishnikov).
Siberian Journal of Numerical Mathematics, Vol. 1 (1998),
no. 2, pp. 153170.
to the top
Publications in Refereed Conference Proceedings

Highorder boundary element method for electromagnetic
scattering at nonsmooth surfaces (with N. Heuer).
"Proceedings of the 10th International Conference on
the Mathematical and Numerical Aspects of Waves; Vancouver, Canada,
July 2529, 2011",
ed. by N. Nigam, Pacific Institute for the Mathematical Sciences,
Canada, 2011, pp. 121124.

The pversion 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. 145152.

Optimal a priori error estimate for the pversion of the BEM on open
surfaces (with N. Heuer).
"Proceedings of the International Conference on Computational
Mathematics, ICCM2004. Part II",
ed. by G. A. Mikhailov, V. P. Il'in, and Y. M. Laevsky, ICM&MG Publishers,
Novosibirsk, Russia, 2004, pp. 794799.

An exponential rate of convergence of the finite element method for the
Dirichlet problem with singularity of a solution (with V. A. Rukavishnikov).
"ENUMATH99. Proceedings of the Third European Conference on Numerical
Mathematics and Advanced Applications, Jyvaskyla, Finland, July 2630,
1999", ed. by P. Neittaanmaki, T. Tiihonen and P. Tarvainen,
World Scientific, Singapore, 2000, pp. 681689.

On the hp version of the finite element method using singular
functions (with V. A. Rukavishnikov).
"The FarEastern SchoolSeminar on Mathematical Modeling and Numerical
Analysis. The Proceedings &Abstracts",
ed. by V. A. Rukavishnikov, Khabarovsk, 1999, pp. 613.