Embedded Files
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.
Book Chapters:
Book Chapters:
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.
Preprints:
Preprints:
A. Demlow. A mixed quasi-trace surface finite element method for the Laplace-Beltrami problem. Submitted.
Refereed Publications:
Refereed Publications:
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)
Unpublished lecture notes:
Unpublished lecture notes:
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.
Page updated
Report abuse