Preprints (my arXiv)
- with Gerard Awanou. On uniqueness of weak solutions to the second boundary value problem for generated prescribed Jacobian equations [arXiv] 2021.
- with Vladmir Sicca Gonçalves. A prescribed scalar and boundary mean curvature problem on compact manifolds with boundary [arXiv] 2021.
- On the convergence theory of adaptive mixed finite element methods for the Stokes problem [arxiv] 2014.
- with Michael Holst and Yunrong Zhu. Local convergence of adaptive methods for nonlinear partial differential equations [arXiv] 2010.
Journal articles
- with Ibrahim Al Balushi, Wen Jiang and Tae-Yeon Kim. A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean [link]. Computer Methods in Applied Mechanics and Engineering, 371:113317 (2020).
- with Erick Schulz. Convergence of discrete exterior calculus approximations for Poisson problems [arxiv]. Discrete & Computational Geometry, 63(2):346–376 (2020).
- with Michael Holst and Caleb Meier. Non-CMC solutions of the Einstein constraint equations on compact manifolds with apparent horizon boundaries [arXiv]. Communications in Mathematical Physics, 357(2):467–517 (2018).
- with Ibrahim Al Balushi, Wen Jiang and Tae-Yeon Kim. Adaptivity of a B-spline based finite element method for modeling wind-driven ocean circulation [link]. Computer Methods in Applied Mechanics and Engineering, 332:1–24 (2018).
- Convergence rates of adaptive methods, Besov spaces, and multilevel approximation [arxiv]. Foundations of Computational Mathematics, 17(4), 917-956 (2017).
- with Rustum Choksi and Ihsan Topaloglu. Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere [arxiv]. ESAIM: Control, Optimisation and Calculus of Variations, 21(1), 247-270 (2015).
- with Douglas Arnold, Richard Falk and Johnny Guzmán. On the consistency of the combinatorial codifferential [arXiv]. Transactions of the American Mathematical Society, 366, 5487-5502 (2014).
- with Michael Holst. The Lichnerowicz equation on compact manifolds with boundary. [arXiv]. Classical and Quantum Gravity, 30, 205011 (2013). Selected as a highlight of the journal in 2013-2014.
- Adaptive boundary element methods with convergence rates [arXiv]. Numerische Mathematik, 124(3), 471-516 (2013).
- with Michael Holst and Evelyn Lunasin. Analysis of a general family of regularized Navier-Stokes and magnetohydrodynamics models [arXiv]. Journal of Nonlinear Science, 20(5), 523-567 (2010).
- with Michael Holst and Gabriel Nagy. Rough solutions of the Einstein constraints on closed manifolds without near-CMC conditions [arXiv]. Communications in Mathematical Physics, 288, 547-613 (2009).
- with Michael Holst and Gabriel Nagy. Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics [arXiv]. Physical Review Letters, 100, 161101 (2008).
- An optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems [pdf]. Journal of Computational and Applied Mathematics, 211(1), 90-102 (2008).
- with Helmut Harbrecht and Rob Stevenson. An optimal adaptive wavelet method without coarsening of the iterands [pdf]. Mathematics of Computation, 76, 615-629 (2007).
- with Rob Stevenson. Computation of singular integral operators in wavelet coordinates [pdf]. Computing, 76, 77-107 (2006).
- with Rob Stevenson. Computation of differential operators in wavelet coordinates [pdf]. Mathematics of Computation, 75, 697-709 (2006).
In preparation
- with Hani Ali. On critical and supercritical regularized Navier-Stokes equations.
- with Young Ju Lee. On a modified Oldroyd-B model.
- with Michael Holst and Yongcheng Zhou. Adaptive coupling of finite element and boundary element methods for a class of nonlinear interface problems.
Thesis
Adaptive wavelet algorithms for solving operator equations
[summary |
samenvatting |
main part (1.6M)].
PhD thesis. Department of Mathematics, Utrecht University. August 2006. ISBN 90-393-4365-9.
[errata for the printed version]
Talks
2019
- On convergence of discrete exterior calculus. Oberwolfach workshop on Innovative Algorithms. Oberwolfach. September 6, 2019.
- Einstein constraint equations. Mongolian Academy of Sciences. Ulan Bator. July 5, 2019.
- On analysis of discrete exterior calculus. AMS Sectional Meeting. Honolulu. March 24, 2019.
2018
- Elliptic estimates for operators with nonsmooth coefficients. Capital Normal University. Bejing. China. July 23, 2018.
- A prescribed scalar-mean curvature problem. Chinese Academy of Sciences. Bejing. China. July 23, 2018.
- Elliptic estimates for operators with nonsmooth coefficients. International Conference on Partial Differential Equations. Changchun. China. July 18-21, 2018.
- A prescribed scalar-mean curvature problem. National University of Mongolia. Ulan Bator. Mongolia. July 5, 2018.
- On analysis of discrete exterior calculus. Huazhong University of Science and Technology. Wuhan. China. June 21, 2018.
- Elliptic estimates for operators with nonsmooth coefficients. Wuhan University. Wuhan. China. June 21, 2018.
- Some scaling estimates in Besov and Triebel-Lizorkin spaces. McGill Geometric Analysis Seminar. February 7, 2018.
- Elliptic estimates for operators with nonsmooth coefficients. Workshop on General Relativity and Finite Element Exterior Calculus. University of California, San Digeo. January 13-16, 2018.
2017
- Elliptic estimates for operators with rough coefficients. McGill Geometric Analysis Seminar. September 27, 2017.
- On analysis of discrete exterior calculus. BIRS Workshop on Geometric Numerical Integration and Structure-Preserving Discretization. Banff. June 11-16, 2017.
- On analysis of discrete exterior calculus. Trimester Seminar. Hausdroff Research Instritute for Mathematics. Bonn. April 20, 2017.
2016
- A prescribed scalar-mean curvature problem. Session on Geometric PDEs. Canadian Mathematical Society Winter Meeting. Niagara Falls. December 2-5, 2016.
- Approximation properties of finite element exterior calculus. Session on Structure-Preserving Discretizations. Canadian Mathematical Society Winter Meeting. Niagara Falls. December 2-5, 2016.
- On approximation classes of adaptive methods. Oberwolfach workshop on Adaptive Algorithms. Oberwolfach. September 22, 2016.
- Well posedness theory for some regularized models of turbulence. PDE Seminar. National University of Mongolia. Ulan Bator. July 29, 2016.
2015
- Well posedness theory for some regularized models of turbulence. Session on Nonlinear Evolutionary Equations. Canadian Mathematical Society Winter Meeting. Montreal. December 6, 2015.
- On analysis of discrete exterior calculus. Computational Mathematics Seminar. University of Pittsburgh. Pittsburgh. November 10, 2015.
- On analysis of discrete exterior calculus. Applied Mathematics Seminar. University of Leicester. Leicester. October 29, 2015.
- On analysis of discrete exterior calculus. Scientific Computation Seminar. University of Nottingham. Nottingham. October 28, 2015.
- On approximation classes of adaptive finite element methods. International Congress on Industrial and Applied Mathematics. Beijing. August 14, 2015.
- The Navier-Stokes equations with random initial data. Stochastic Analysis and Applications Mongolia. National University of Mongolia. Ulan Bator. August 6, 2015.
- The Lichnerowicz equation and the prescribed scalar-mean curvature problem in the compact-with-boundary setting. Focus Program on 100 Years of General Relativity. Fields Institute. Toronto. May 13, 2015.
2014
- On approximation classes of adaptive finite element methods [slides]. LMS-EPSRC Durham Symposium. Durham. July 9, 2014.
- Adaptive mixed finite element methods for the Stokes problem. McGill Applied Math Working Seminar. February 25, 2014.
2013
- The Einstein constraint equations on compact manifolds with or without boundary. PIMS-AMI seminar. Edmonton. October 25, 2013.
- Convergence rates of adaptive boundary element methods [slides]. Numerical Analysis & PDE seminar. University of Delaware. May 2, 2013.
- On the consistency of the combinatorial codifferential [slides]. Joint Mathematics Meetings. San Diego. January 11, 2013.
2012
- Adaptive boundary element methods with convergence rates. ESI Workshop on Wavelet Methods in Scientific Computing. Vienna. November 12, 2012.
- On well-posedness of the Navier-Stokes-αβ equations with the wall-eddy boundary conditions [slides]. BIRS Workshop on Regularized and LES Methods for Turbulence. Banff. May 18, 2012.
- Nonconstant mean curvature solutions of the Einstein constraint equations [slides]. CRM Workshop on Geometric PDE. Montreal. April 27, 2012.
- Einstein constraint equations. McGill Applied Math Working Seminar. March 14, 2012.
- Einstein field equations. McGill Applied Math Working Seminar. Montreal. February 8, 2012.
2011
- Adaptive boundary element methods with convergence rates. SIAM Conference on Analysis of PDEs. San Diego. November 14, 2011.
- Partial regularity results for generalized alpha models of turbulence [slides]. SIAM Conference on Analysis of PDEs. San Diego. November 14, 2011.
- Adaptive boundary element methods with convergence rates [slides]. CRM-McGill Applied Mathematics Seminar. Montreal. September 19, 2011.
- Generalized Navier-Stokes type models. McGill Applied Math Working Seminar. Montreal. September 14, 2011.
2010
- Wavelet Galerkin methods. Applied Mathematics Seminar. National University of Mongolia. Ulan Bator. June 9, 2010.
- Einstein's constraint equations. Analysis Seminar. National University of Mongolia. Ulan Bator. June 7, 2010.
- Partial regularity for generalized Navier-Stokes equations. McGill Analysis Seminar. McGill University. Montreal. Febuary 12, 2010.
- Mathematical general relativity [slides]. Winter school in pure and applied math. McGill University. Montreal. January 8-11, 2010.
2009
- Local convergence of adaptive finite element methods for nonlinear problems [slides]. CRM-McGill Applied Mathematics Seminar. Montreal. November 23, 2009.
- Solutions of the Einstein constraint equations on asymptotically Euclidean manifolds. 25th Pacific Coast Gravity Meeting. University of Oregon, Eugene. March 27-28, 2009.
- On analysis and numerical treatment of Einstein's constraint equations in general relativity [slides]. CRM-McGill Applied Mathematics Seminar. McGill University. Montreal. Canada. February 13, 2009.
2008
- Finite elements for the Lichnerowicz equation. Mathematical and Computational Physics Group Meeting. University of California, San Diego. April 21, 2008.
- Non-constant mean curvature solutions to Einstein's constraint equations: A fixed point argument [slides]. 24th Pacific Coast Gravity Meeting. University of California, Santa Barbara. March 21-22, 2008.
- Analysis and convergent adaptive solution of the Einstein constraint equations [slides]. Workshop on Adaptive Numerical Methods for PDE's. Wolfgang Pauli Institute. Vienna University. Austria. January 21-25, 2008.
- A short tour of Sobolev spaces. Mathematical and Computational Physics Group Meeting. University of California, San Diego. February 27, 2008.
2007
- Einstein constraints on closed manifolds. Mathematical and Computational Physics Group Meeting. University of California, San Diego. October 24, 2007.
- A priori estimates for Petrov-Galerkin approximation on Riemannian manifolds. Mathematical and Computational Physics Group Meeting. University of California, San Diego. June 7, 2007.
- Wavelet methods for operator equations. Mathematical and Computational Physics Group Meeting. University of California, San Diego. February 6, 2007.
2006
- Adaptive wavelet algorithms for solving operator equations [slides]. General Mathematical Colloquium. Mathematisch Instituut. Universiteit Utrecht. September 21, 2006.
- Adaptive wavelet algorithms with truncated residuals [slides]. EC-IHP Breaking Complexity Final Meeting. Wolfgang Pauli Institute. Vienna University. Austria. September 14-18, 2006.
- Adaptive wavelet methods with truncated residuals. Postgraduate seminar IGPM. RWTH Aachen. Germany. August 31, 2006.
- Adaptive wavelet algorithms for solving operator equations. International Conference on Multilevel Iterative Methods. Peking University. Beijing. China. August 14-18, 2006.
- Adaptive wavelet methods with truncated residuals. EC-IHP Breaking Complexity Spring Meeting. Politecnico di Torino. Turin. Italy. April 20-22, 2006.
- An optimal adaptive wavelet method without coarsening of the iterands [slides]. Joint HASSIP/DFG-SPP1114 Workshop "Recent Progress in Wavelet Analysis and Frame Theory". Universität Bremen. Bremen. Germany. January 23-26, 2006.
2005
- An optimal adaptive wavelet method for strongly elliptic operator equations [slides]. Workshop on Fast Numerical Solution of PDE's. Mathematisch Instituut. Universiteit Utrecht. December 20-22, 2005.
- Optimal adaptive wavelet methods for linear operator equations [slides for screen, for printer]. Biweekly numerical mathematics colloquium. Mathematisch Instituut. Universiteit Utrecht. June 17, 2005.
2004
- Computation of operators in wavelet coordinates [slides]. EC-IHP Breaking Complexity Mid-Term Meeting. Istituto di Matematica Applicata alle Tecnologie Industriali. Pavia. Italy. December 9 - 10, 2004.
- Computation of operators in wavelet coordinates [slides]. 6th Minisimposium "Topics In and Around Numerical Analysis". KdV Institute for Mathematics. Amsterdam. October 27, 2004.