![]() Kiss, Gergely ![]() Scientific Conference (2018, June) Detailed reference viewed: 44 (0 UL)![]() ; Poncin, Norbert ![]() in Indagationes Mathematicae (2005), 16(2), 181--200 Detailed reference viewed: 126 (3 UL)![]() Poncin, Norbert ![]() Scientific Conference (2004) Detailed reference viewed: 116 (2 UL)![]() Thalmaier, Anton ![]() ![]() in Annals of Probability (2019), 47(2), 743-773 Detailed reference viewed: 528 (110 UL)![]() Thalmaier, Anton ![]() in Potential Analysis (2004), 20(2), 105-123 Detailed reference viewed: 289 (27 UL)![]() Bordas, Stéphane ![]() in Computer Methods in Applied Mechanics and Engineering (2007), 196(35-36), 3381-3399 This paper is the first attempt at error estimation for extended finite elements. The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity ... [more ▼] This paper is the first attempt at error estimation for extended finite elements. The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity enriched finite element methods such as the extended finite element method (XFEM). In each element, the local estimator is the L2 norm of the difference between the raw XFEM strain field and an enhanced strain field computed by extended moving least squares (XMLS) derivative recovery obtained from the raw nodal XFEM displacements. The XMLS construction is tailored to the nature of the solution. The technique is applied to linear elastic fracture mechanics, in which near-tip asymptotic functions are added to the MLS basis. The XMLS shape functions are constructed from weight functions following the diffraction criterion to represent the discontinuity. The result is a very smooth enhanced strain solution including the singularity at the crack tip. Results are shown for two- and three-dimensional linear elastic fracture mechanics problems in mode I and mixed mode. The effectivity index of the estimator is close to 1 and improves upon mesh refinement for the studied near-tip problem. It is also shown that for the linear elastic fracture mechanics problems treated, the proposed estimator outperforms one of the superconvergent patch recovery technique of Zienkiewicz and Zhu, which is only C0. Parametric studies of the general performance of the estimator are also carried out. © 2007 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 202 (6 UL)![]() Marichal, Jean-Luc ![]() in Rocky Mountain Journal of Mathematics (2007), 37(2), 551-571 We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r=d V/A. We show that the families of regions for which this formula for r ... [more ▼] We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r=d V/A. We show that the families of regions for which this formula for r is valid, which we call homogeneous families, include all the families of similar regions. We determine equivalent conditions for a family to be homogeneous, provide examples of homogeneous families made up of non-similar regions, and offer a geometric interpretation of r in a few cases. [less ▲] Detailed reference viewed: 41 (2 UL)![]() Marichal, Jean-Luc ![]() Presentation (2005, April 08) Detailed reference viewed: 33 (1 UL)![]() Marichal, Jean-Luc ![]() Presentation (2003, October 21) We explore the idea that the derivative of the volume, V , of a region in Rp with respect to r equals its surface area, A, where r = p V/A. We show that the families of regions for which this formula for ... [more ▼] We explore the idea that the derivative of the volume, V , of a region in Rp with respect to r equals its surface area, A, where r = p V/A. We show that the families of regions for which this formula for r is valid, which we call homogeneous families, include all the families of similar regions. We determine equivalent conditions for a family to be homogeneous, provide examples of homogeneous families made up of non-similar regions, and offer a geometric interpretation of r in a few cases. [less ▲] Detailed reference viewed: 83 (1 UL)![]() Nabilou, Hossein ![]() in Banking & Finance Law Review (2016), 32(1), 203-207 Detailed reference viewed: 87 (11 UL)![]() Thompson, James ![]() in Journal of Theoretical Probability (2019) We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of ... [more ▼] We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, although the assumptions are purely geometric. [less ▲] Detailed reference viewed: 263 (67 UL)![]() Govzmann, Alisa ![]() Doctoral thesis (2023) Detailed reference viewed: 30 (2 UL)![]() Belmans, Pieter ![]() in Michigan Mathematical Journal (2023) Detailed reference viewed: 26 (0 UL)![]() Belmans, Pieter ![]() in Proc. Lond. Math. Soc. (3) (2022), 125(6), 1452--1482 Detailed reference viewed: 17 (0 UL)![]() Belmans, Pieter ![]() in Transformation Groups (2021) Detailed reference viewed: 15 (0 UL)![]() Schapira, Pierre ![]() E-print/Working paper (2013) Detailed reference viewed: 52 (1 UL)![]() Poncin, Norbert ![]() Presentation (2018, September 18) Detailed reference viewed: 153 (3 UL)![]() Bonavolonta, Giuseppe ![]() Doctoral thesis (2013) Detailed reference viewed: 136 (14 UL)![]() Poncin, Norbert ![]() Presentation (2014) Detailed reference viewed: 157 (13 UL)![]() Scherotzke, Sarah ![]() in Bulletin of the London Mathematical Society (2022), 54(1), 264-274 Detailed reference viewed: 29 (0 UL) |
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