focus areas:

nonlinear and higher order problems

S. Pollock, Uniqueness of discrete solutions to nonmonotone quasilinear PDE in 2D and 3D on nonobtuse meshes, Submitted, 2018.

C. Evans, S. Pollock, L. G. Rebholz and M. Xiao, A proof that Anderson acceleration increases the convergence rate in linearly converging fixed point methods (but not in quadratically converging ones), Submitted, 2018. preprint: arXiv:math.NA/1810.08455.

S. Pollock, L. G. Rebholz and M. Xiao, Anderson-accelerated convergence of Picard iterations for
incompressible Navier-Stokes equations, SIAM J. Numer. Anal., 57(2), 615–637, 2019.
DOI: 10.1137/18M1206151.   preprint: arXiv:math.NA/1810.08494.   pdf (Copyright © by SIAM)

S. Pollock, Y. Zhu, A matrix analysis approach to discrete comparison principles for nonmonotone PDE, Accepted, Numer. Algor., 2019.
DOI:10.1007/s11075-019-00713-x . preprint: arXiv:math.NA/1711.07506. publisher’s full-text (view only).

S. Pollock, Y. Zhu, Discrete comparison principles for quasilinear elliptic PDE, Submitted, 2018.
preprint: arXiv:math.NA/1708.02301.

S. Pollock, Y. Zhu, Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition, Numer. Math., 139 (4), p. 845-865, 2018.
DOI: 10.1007/s00211-018-0956-4.   preprint: arXiv:math.NA/1704.04319.

S. Pollock, Stabilized and inexact adaptive methods for capturing internal layers in quasilinear PDE, J. Comput. Appl. Math., 308, p 243-262, 2016.
DOI: 10.1016/   preprint: arXiv:math.NA/1507.06965.

S. Brenner, M. Oh, S. Pollock, K. Porwal, M. Schedensack, N. Sharma, A C^0 interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints, in Topics in Numerical Partial Differential Equations and Scientific Computing, p 1-22, S. Brenner, ed, IMA Volumes in Mathematics and Its Applications, 160, 2016

S. Pollock, An improved method for solving quasilinear convection diffusion problems, SIAM J. Sci. Comput., 38-2, p A1121-A1145, 2016.
DOI: 10.1137/15M1007823.   preprint: arXiv:math.NA/1502.02629.

S. Pollock, A regularized Newton-like method for nonlinear PDE, Numer. Func. Anal. Opt., 36(11), p 1493-1511, 2015.
DOI: 10.1080/01630563.2015.1069328.   preprint: arXiv:math.NA/1412.6487.

multiscale methods and goal-oriented adaptivity

E. Chung, S. Pollock, S. M. Pun, Online basis construction for goal-oriented adaptivity in the Generalized Multiscale Finite Element Method. Accepted, J. Comput. Phys., 2019.
DOI: 10.1016/ preprint: arXiv:math.NA/1812.02290

E. T. Chung, S. Pollock, S. M. Pun, Goal-oriented adaptivity of mixed GMsFEM for flows in heterogeneous media, Comput. Methods Appl. Mech. Eng., 323, p 151-173, 2017.
DOI: 10.1016/j.cma.2017.05.019

E.T. Chung, W.T. Leung, S. Pollock, Goal-oriented adaptivity for GMsFEM, J. Comput. Appl. Math., 296, p 625-637, 2016.
DOI: 10.1016/   preprint: arXiv:math.NA/1509.05643.

M. Holst, S. Pollock, and Y. Zhu, Convergence of goal-oriented adaptive finite element methods for semilinear problems, Comp. Vis. Sci., 17(1), p 43-63, 2015.
DOI: 10.1007/s00791-015-0243-1.   preprint: arXiv:math.NA/1203.1381.

M. Holst and S. Pollock, Convergence of goal-oriented adaptive finite element methods for nonsymmetric problems, Numer. Meth. Part. D.E., 32(2), p 479-509, 2016.
DOI: 10.1002/num.22002.   preprint: arXiv:math.NA/1108.3660.

inverse kinematics

E. A. Coutsias, K. W. Lexa, M. J. Wester, S. N. Pollock, M. P. Jacobson, Exhaustive conformational sampling of complex fused ring macrocycles using inverse kinematics, J. Chem. Theory Comput., 12 (9), p 4674-4687, 2016.
DOI: 10.1021/acs.jctc.6b00250

W.M. Brown, S. Martin, S.N. Pollock, E.A. Coutsias, J.P. Watson, Algorithmic dimensionality reduction for molecular structure analysis, J. Chem. Phys. 129(6): 064118, 2008.
DOI: 10.1063/1.2968610.

S.N. Pollock, E.A. Coutsias, M.J. Wester and T.I. Oprea, Scaffold topologies I: exhaustive enumeration up to eight rings, J. Chem. Inf. Model, 48(7), p. 1304-1310, 2008.
DOI: 10.1021/ci7003412.

M.J. Wester, S.N. Pollock, E.A. Coutsias, T.K. Allu, S. Muresan and T.I. Oprea, Scaffold topologies II: analysis of chemical databases, J. Chem Inf. Model., 48(7), p. 1311-1324, 2008.
DOI: 10.1021/ci700342h.