Zobrazeno 1 - 10
of 533
pro vyhledávání: '"Ern, Alexandre"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G9, Pp 1521-1530 (2023)
This paper studies the unique continuation problem for the heat equation. We prove a so-called conditional stability estimate for the solution. We are interested in local estimates that are Hölder stable with the weakest possible norms of data on th
Externí odkaz:
https://doaj.org/article/82abfb8bd3ad43f28b163b5819686067
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G4, Pp 723-736 (2023)
We estimate best-approximation errors using vector-valued finite elements for fields with low regularity in the scale of the fractional-order Sobolev spaces. By assuming that the target field enjoys an additional integrability property on its curl or
Externí odkaz:
https://doaj.org/article/24458807064a4dff8273546773d53cdf
Autor:
Dong, Zhaonan, Ern, Alexandre
We present both $hp$-a priori and $hp$-a posteriori error analysis of a mixed-order hybrid high-order (HHO) method to approximate second-order elliptic problems on simplicial meshes. Our main result on the $hp$-a priori error analysis is a $\frac12$-
Externí odkaz:
http://arxiv.org/abs/2410.02540
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 9-10, Pp 1101-1110 (2021)
We prove that the minimizer in the Nédélec polynomial space of some degree $p\ge 0$ of a discrete minimization problem performs as well as the continuous minimizer in $H({\bf curl})$, up to a constant that is independent of the polynomial degree $p
Externí odkaz:
https://doaj.org/article/0c81c05f4a174e34be9b519dfc066dec
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equ
Externí odkaz:
http://arxiv.org/abs/2407.02433
We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of the method i
Externí odkaz:
http://arxiv.org/abs/2307.11541
Autor:
Dong, Zhaonan, Ern, Alexandre
We devise and analyze $C^0$-conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. $C^0$-conforming HHO methods hinge on cell unknowns which are $C^0$-conforming poly
Externí odkaz:
http://arxiv.org/abs/2206.07074
We estimate best-approximation errors using vector-valued finite elements for fields with low regularity in the scale of fractional-order Sobolev spaces. By assuming additionally that the target field has a curl or divergence property, we establish u
Externí odkaz:
http://arxiv.org/abs/2201.01708
Autor:
Dong, Zhaonan, Ern, Alexandre
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to w
Externí odkaz:
http://arxiv.org/abs/2108.08348
This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlying the mathematical analysis, and some useful variants of the method a
Externí odkaz:
http://arxiv.org/abs/2106.09348