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Author (up) Aylwin, R.; Jerez-Hanckes, C. doi  openurl
  Title Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains Type
  Year 2023 Publication SIAM Journal on Numerical Analysis Abbreviated Journal SIAM J. Numer. Anal.  
  Volume 61 Issue 3 Pages 1139-1171  
  Keywords Ne'; de'; lec finite elements; curl-conforming elements; Maxwell equations; proximation; Strang lemma  
  Abstract We consider the problem of domain approximation in finite element methods for Maxwell equations on curved domains, i.e., when affine or polynomial meshes fail to exactly cover the domain of interest. In such cases, one is forced to approximate the domain by a sequence of polyhedral domains arising from inexact meshes. We deduce conditions on the quality of these approximations that ensure rates of error convergence between discrete solutions -- in the approximate domains -- to the continuous one in the original domain.  
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  Series Volume Series Issue Edition  
  ISSN 0036-1429 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001044149800001 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1700  
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Author (up) Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. doi  openurl
  Title Optimal Operator Preconditioning For Galerkin Boundary Element Methods On 3D Screens Type
  Year 2020 Publication SIAM Journal on Numerical Analysis Abbreviated Journal SIAM J. Numer. Anal.  
  Volume 58 Issue 1 Pages 834-857  
  Keywords  
  Abstract We consider first-kind weakly singular and hypersingular boundary integral operators for the Laplacian on screens in $\mathbb{R}^{3}$ and their Galerkin discretization by means of low-order piecewise polynomial boundary elements. For the resulting linear systems of equations we propose novel Calderón-type preconditioners based on (i) new boundary integral operators, which provide the exact inverses of the weakly singular and hypersingular operators on flat disks, and (ii) stable duality pairings relying on dual meshes. On screens obtained as images of the unit disk under bi-Lipschitz transformations, this approach achieves condition numbers uniformly bounded in the meshwidth even on locally refined meshes. Comprehensive numerical tests also confirm its excellent preasymptotic performance.  
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  Corporate Author Thesis  
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  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0036-1429 ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1011  
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