Roles and subjects

Retained Lecturer in Mathematics

Contact

charles.parker@maths.ox.ac.uk

Academic Background

I completed a Bachelor of Science in both mathematics and computer science at the University of Maryland, College Park and a PhD in applied mathematics at Brown University under the supervision of Mark Ainsworth. I currently hold a Mathematical Sciences Postdoctoral Research Fellowship from the National Science Foundation.

Undergraduate Teaching Areas

• Applied Mathematics

Research Interests

I am broadly interested the numerical analysis of partial differential equations. More specifically, I focus on the theory and implementation of finite element methods.

Publications

1. C. Parker and E. Süli, Stable lifting of polynomial traces on triangles, SIAM Numer. Anal., to appear, https://arxiv.org/abs/2304.13074.
2. M. Ainsworth and C. Parker, Uniform preconditioners for high order finite element approximations of planar linear elasticity, Math. Comp., to appear, https://arxiv.org/abs/2302.04306.
3. M. Ainsworth and C. Parker, Statically condensed iterated penalty method for high order finite element discretizations of incompressible flow, SIAM J. Sci. Comput., to appear, https://arxiv.org/abs/2301.01818.
4. M. Ainsworth and C. Parker, Unlocking the secrets of locking: Finite element analysis in planar linear elasticity, Comput. Methods Appl. Mech. Engrg., 395 (2022), doi:10.1016/j.cma.2022.115034.
5. M. Ainsworth and C. Parker, A mass conserving mixed hp-FEM scheme for Stokes flow. Part III: Implementation and preconditioning, SIAM J. Numer. Anal., 60 (2022), doi:10.1137/21M1433927.
6. M. Ainsworth and C. Parker, Preconditioning high order H² conforming finite elements on triangles. Numer. Math., 148 (2021), doi:10.1007/s0021-021-01206-7.
7. M. Ainsworth and C. Parker, Mass conserving mixed hp-FEM approximations to Stokes flow. Part II: Optimal convergence, SIAM J. Numer. Anal., 59 (2021), doi:10.1137/20M1359110.
8. M. Ainsworth and C. Parker, Mass conserving mixed hp-FEM approximations to Stokes flow. Part I: Uniform stability, SIAM J. Numer. Anal., 59 (2021), doi:10.1137/20M1359109.
9. M. Ainsworth and C. Parker, H²-stable polynomial liftings on triangles, SIAM J. Numer. Anal., 58 (2020), doi:10.1137/19M128171X.