Zhaonan (Peter) Dong

Research Associate

Department of Mathematics
University of Leicester
University Road 
Leicester, LE1 7RH
United Kingdom

tel: +44 (0) 116 252 5060
email: zd14@le.ac.uk

Personal Website

I left the University of Leicester in November 2018.

Email (Personal): dznpeter@gmail.com

Personal details:

• 09/2012-09/2016: PhD in Applied Mathematics. The supervisors: Prof Emmanuil H. Georgoulis and Dr Andrea Cangiani.  University of Leicester, UK.

• 09/2016-09/2018: Post-doc Research Associate in the Department of Mathematics, University of Leicester.

Research Interest:

• Numerical Methods for Partial Differential Equations: Finite Element Methods (FEM). More specifically: continuous and discontinuous FEM, hp-version FEM, adaptive algorithms, polygonal discretization method.

• Approximation Theory: Multivariate polynomials, radial basis functions.

Publications

Monograph

1. A. Cangiani,  Z. Dong, E. H. Georgoulis, and P. Houston.

hp–Version discontinuous Galerkin methods on polygonal and polyhedral meshes. SpringerBriefs in Mathematics (2017)

Chapters in peer-reviewed volumes

1. P. F. Antonietti, A. Cangiani, J Collis, Z. Dong, E. H. Georgoulis, S. Giani and P. Houston.

Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. In Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering, Springer (2016).

Articles in peer-reviewed journals

1. A. Cangiani, Z. Dong, E. H. Georgoulis and P. Houston.

hp–Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis. 50(3) pp. 699-725, (2016). PDF

2. A. Cangiani, Z. Dong and E. H. Georgoulis.

hp–Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM Journal on Scientific Computing. 39(4) pp.A1251–A1279 (2017). PDF

3. Z. Dong, E. H. Georgoulis, J. Levesley and F. Usta.

A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. Computers and Mathematics with Applications., 76(8) pp.A1950-A1965 (2018).

4. Z. Dong.

On the exponent of exponential convergence of p-version finite element spaces. Submitted for publication. Advances in Computational Mathematics. Published online, 2018. DOI: 10.1007/s10444-018-9637-1. PDF

5. Z. Dong.

Discontinuous Galerkin methods for the biharmonic problem on polygonal and polyhedral meshes. International Journal of Numerical Analysis and Modeling. Accepted for publication. PDF

6. Z. Dong, E. H. Georgoulis, and T. Pryer.

Recovered finite element methods on polygonal and polyhedral meshes. Submitted for publication. PDF

Other publications

1. Z. Dong, E. H. Georgoulis, J. Levesley and F. Usta.

Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration. arXiv preprint arXiv:1501.03296 (2015). PDF

2. Z. Dong.

Discontinuous Galerkin Methods on Polytopic Meshes. D.Phil. Thesis, Department of Mathematics, University of Leicester (2016).