Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Alan Demlow"'
Publikováno v:
IMA Journal of Numerical Analysis.
We prove residual-type a posteriori error estimates in the maximum norm for a linear scalar elliptic convection–diffusion problem that may be singularly perturbed. Similar error analysis in the energy norm by Verfürth indicates that a dual norm of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7c587a08807b0a80ee7dd46fa70bed97
https://doi.org/10.1093/imanum/drad001
https://doi.org/10.1093/imanum/drad001
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to the Laplace–Beltrami problem posed on an n-dimensional surface γ emb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8fc81618166a21f394dc2ec0daf9ea4d
https://doi.org/10.1016/bs.hna.2019.06.002
https://doi.org/10.1016/bs.hna.2019.06.002
Autor:
Alan Demlow
Publikováno v:
Numerische Mathematik. 136:941-971
Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework also relies e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f90e0ac876328aa8fe75d7fceff2e71
https://doi.org/10.1007/s00211-016-0862-6
https://doi.org/10.1007/s00211-016-0862-6
The Stokes equation posed on surfaces is important in some physical models, but its numerical solution poses several challenges not encountered in the corresponding Euclidean setting. These include the fact that the velocity vector should be tangent
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d44a126e3122878c816f7c821155974a
http://arxiv.org/abs/1908.11460
http://arxiv.org/abs/1908.11460
Autor:
Bernardo Cockburn, Alan Demlow
Publikováno v:
Mathematics of Computation. 85:2609-2638
We define and analyze hybridizable discontinuous Galerkin methods for the Laplace-Beltrami problem on implicitly defined surfaces. We show that the methods can retain the same convergence and superconvergence properties they enjoy in the case of flat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7eb41a5affcadf372d6268067ad43d35
https://doi.org/10.1090/mcom/3093
https://doi.org/10.1090/mcom/3093
Autor:
Alan Demlow, Andrea Bonito
We prove new a posteriori error estimates for surface finite element methods (SFEM). Surface FEM approximate solutions to PDE posed on surfaces. Prototypical examples are elliptic PDE involving the Laplace-Beltrami operator. Typically the surface is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd2541e3fa1fd557e59ca324e99335ad
Elliptic partial differential equations on surfaces play an essential role in geometry, relativity theory, phase transitions, materials science, image processing, and other applications. They are typically governed by the Laplace-Beltrami operator. W
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::17b465d283e3763ae0fbb1d39b71e642
http://arxiv.org/abs/1801.00197
http://arxiv.org/abs/1801.00197
Autor:
Alan Demlow
Publikováno v:
Numerische Mathematik. 134:27-60
A rich theory demonstrating convergence and optimality of adaptive finite element methods (AFEM) has been developed in recent years. In this work we prove optimality of AFEM which are designed to control local energy errors in elliptic partial differ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::75b9ff398d34bd50222265f075a38803
https://doi.org/10.1007/s00211-015-0774-x
https://doi.org/10.1007/s00211-015-0774-x
Autor:
Natalia Kopteva, Alan Demlow
Publikováno v:
Numerische Mathematik. 133:707-742
Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. Standard finite element approximations are considered. The error constants are inde
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::48f7301a9d1332dabb78a0e53797b4ac
https://doi.org/10.1007/s00211-015-0763-0
https://doi.org/10.1007/s00211-015-0763-0
Autor:
Alan Demlow, Fernando Camacho
Publikováno v:
IMA Journal of Numerical Analysis. 35:1199-1227
Surface Finite Element Methods (SFEM) are widely used to solve surface partial differential equations arising in applications including crystal growth, fluid mechanics and computer graphics. A posteriori error estimators are computable measures of th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d893942efe53a457bcdf159e6457ea9e
https://doi.org/10.1093/imanum/dru036
https://doi.org/10.1093/imanum/dru036