Much of this material is based upon work supported by the National Science Foundation under grants DMS-0303378, DMS-0713770, DMS-1016094, DMS-1318652/1518925, DMS-1720369, and DMS-2012326. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
1. A. Bonito, A. Demlow, and R.H. Nochetto, Finite element methods for the Laplace-Beltrami operator. Handbook of Numerical Analysis, Volume XXI: Geometric PDEs-, Part I, (eds) A. Bonito and R.H. Nochetto, 1-103, 2020.
A. Demlow. A mixed quasi-trace surface finite element method for the Laplace-Beltrami problem. Submitted.
29. A. Demlow and M. Neilan. A tangential and penalty-free finite element method for the surface Stokes problem. SIAM J. Numer. Anal., accepted.
28. A. Demlow, S. Franz, and N. Kopteva. Maximum norm a posteriori error estimates for convection-diffusion problems. IMA J. Numer. Anal., published electronically February 2023.
Final version (published under Open Access)
27. A. Bonito, A. Demlow, and M. Licht, A divergence-conforming finite element method for the surface Stokes equation. SIAM J. Numer. Anal. 58 (2020), 2764-2698.
26. A. Bonito and A. Demlow, A posteriori error estimates for the Laplace-Beltrami operator on parametric C2 surfaces, SIAM J. Numer. Anal. 57 (2019), 973-996.
25. A. Bonito, A. Demlow, and J. Owen, A priori error estimates for finite element approximations to eigenvalues and eigenfunctions of the Laplace-Beltrami operator, SIAM J. Numer. Anal. 56 (2018), 2693-2988.
24. A. Demlow, Convergence and quasi-optimality of adaptive finite element methods for harmonic forms, Numer. Math. 136 (2017), 941-971.
23. A. Bonito and A. Demlow, Convergence and optimality of higher-order adaptive finite element methods for eigenvalue clusters, SIAM J. Numer. Anal. 54 (2016), 2379-2388.
22. A. Demlow. Quasi-optimality of adaptive finite element methods for controlling local energy errors, Numer. Math. 134 (2016), 27-60.
Preprint (PDF)
21. B. Cockburn and A. Demlow, Hybridizable discontinuous Galerkin methods and mixed finite element methods for elliptic problems on surfaces, Math. Comp. 85 (2016), 2609-2638.
Preprint (PDF, 7/15)
20. A. Demlow and N. Kopteva. Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems, Numer. Math. 133 (2016), 707-742.
Preprint (PDF, updated 7/15)
19. F. Camacho and A. Demlow, $L_2$ and pointwise a posteriori error estimates for FEM for elliptic PDEs on surfaces, IMA J. Numer. Anal. 35 (2015), 1199-1227.
Preprint (PDF, substantial revisions 3/14)
18. A. Demlow and A. Hirani, A posteriori error estimates for finite element exterior calculus: The de Rham complex, Found. Comput. Math. 14 (2014), 1337-1371.
17. A. Demlow and S. Larsson, Local pointwise a posteriori gradient error bounds for the Stokes equation, Math. Comp. 82 (2013), 625--649.
Preprint (PDF, updated 9/11)
16. A. Demlow and E. Georgoulis, Pointwise a posteriori error control for discontinuous Galerkin methods for elliptic problems, SIAM. J. Numer. Anal., SIAM J. Numer. Anal. 50 (2012), 2159-2181.
Preprint (PDF; minor revisions 5/12)
15. A. Demlow and M. Olshanskii, An adaptive surface finite element method based on volume meshes, SIAM. J. Numer. Anal. 50 (2012), 1624-1647.
Preprint (PDF, minor revisions 2/12)
14. A. Demlow, D. Leykekhman, A.H. Schatz, and L.B. Wahlbin, Best approximation property in the $W_\infty^1$ norm on graded meshes, Math. Comp. 81 (2012), 743-764.
Preprint (PDF, updated 6/11)
13. A. Demlow and R.P. Stevenson, Convergence and quasi-optimality of an adaptive finite element method for controlling $L_2$ errors, Numer. Math. 177 (2011), 125-218.
Preprint (PDF; updated 6/11)
12. A. Demlow, Convergence of an adaptive finite element method for controlling local energy errors, SIAM J. Numer. Anal. 48 (2010), 470-497.
Preprint (PDF; submitted 11/08, revised version 10/09.)
11. A. Demlow and C. Makridakis, Sharply local pointwise a posteriori error estimates for parabolic problems, Math. Comp. 79 (2010), 1233-1262.
Preprint (PDF)
10. A. Demlow, J. Guzmán, and A.H. Schatz, Local energy estimates for the finite element method on sharply varying grids, Math. Comp. 80 (2011), 1-9.
9. A. Demlow, O. Lakkis, and C. Makridakis, A posteriori error estimates in the maximum norm for parabolic problems, SIAM J. Numer. Anal. 47 (2009), 2157-2176.
8. A. Demlow, Higher-order finite element methods and pointwise error estimates for elliptic problems on surfaces, SIAM J. Numer. Anal. 47 (2009), 805-827.
Preprint (PDF)
7. A. Demlow, Sharply localized pointwise and $W_\infty^{-1}$ estimates for finite element methods for quasilinear problems, Math. Comp. 76 (2007), 1725-1741.
Preprint (PDF)
6. A. Demlow and G. Dziuk, An adaptive finite element method for the Laplace-Beltrami operator on surfaces, SIAM J. Numer. Anal. 45 (2007), 421-442.
Preprint (PDF)
5. A. Demlow, Local a posteriori estimates for pointwise gradient errors in finite element methods for elliptic problems, Math. Comp. 76 (2007), 19-42.
Preprint (PDF)
4. A. Demlow, Localized pointwise a posteriori error estimates for gradients of piecewise linear
finite element approximations to second-order quasilinear elliptic problems, SIAM J. Numer. Anal. 44 (2006), no. 2, 494-514.
Article (PDF; copyright held by SIAM, distributed with permission)
3. A. Demlow, Piecewise linear finite element methods are not localized, Math. Comp. 73 (2004), no. 247, 1195-1201.
Preprint (PDF)
2. A. Demlow, Localized pointwise error estimates for mixed finite element methods, Math. Comp. 73 (2004), no. 248, 1623-1653.
Preprint (PDF)
1. A. Demlow, Suboptimal and optimal convergence in mixed finite element methods, SIAM J. Numer. Anal 39 (2002), no. 6, 1938--1953.
Article (PDF, copyright held by SIAM, distributed with permission)
In spring 2016 I taught a seminar course on singular solutions to elliptic PDEs and their approximation by standard and adaptive finite element methods. I provided the students with lecture notes as part of the course. These are included below. They are not highly edited and are distributed as-is.