Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Duran, Ricardo G."'
Autor:
Drelichman, Irene, Duran, Ricardo G.
We prove the stability in weighted $W^{1,1}$ spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt's class $A_1$ and the family of meshes is quasi-u
Externí odkaz:
http://arxiv.org/abs/2403.07934
We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.
Externí odkaz:
http://arxiv.org/abs/2112.03416
Publikováno v:
In Computers and Mathematics with Applications 15 August 2024 168:39-45
Autor:
Drelichman, Irene, Durán, Ricardo G.
We obtain a Bourgain-Br\'ezis-Mironescu formula on the limit behaviour of a modified fractional Sobolev seminorm when $s\nearrow 1$, which is valid in arbitrary bounded domains. In the case of extension domains, we recover the classical result.
Externí odkaz:
http://arxiv.org/abs/2012.14505
In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard finite eleme
Externí odkaz:
http://arxiv.org/abs/1912.04962
We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\mathbf{W}^{1,p}_0(\omega,\Omega) \times L^p(\omega,\Omega)$, where the weight belongs to a certain Muckenhoupt class an
Externí odkaz:
http://arxiv.org/abs/1905.00476
We analyze the approximation by mixed finite element methods of solutions of equations of the form $-\mbox{div\,} (a\nabla u) = g$, where the coefficient $a=a(x)$ can degenerate going to cero or infinity. First, we extend the classic error analysis t
Externí odkaz:
http://arxiv.org/abs/1903.05138
Autor:
Alvarez, María Luz, Durán, Ricardo G.
Publikováno v:
In Applied Numerical Mathematics June 2023 188:146-159
Autor:
Drelichman, Irene, Durán, Ricardo G.
We show that, for certain non-smooth bounded domains $\Omega\subset\mathbb{R}^n$, the real interpolation space $(L^p(\Omega), W^{1,p}(\Omega))_{s,p}$ is the subspace $\widetilde W^{s,p}(\Omega) \subset L^p(\Omega)$ induced by the restricted fractiona
Externí odkaz:
http://arxiv.org/abs/1710.09453
Autor:
Drelichman, Irene, Durán, Ricardo G.
We obtain improved fractional Poincar\'e and Sobolev Poincar\'e inequalities including powers of the distance to the boundary in John, $s$-John domains and H\"older-$\alpha$ domains, and discuss their optimality.
Externí odkaz:
http://arxiv.org/abs/1705.04227