Bilinear interpolation in triangles based upon a Mangeron theorem.
G. M. Nielson, D. J. Mangeron (1981)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
Similarity:
G. M. Nielson, D. J. Mangeron (1981)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
Similarity:
A. Agouzal, N. Debit (2010)
Mathematical Modelling of Natural Phenomena
Similarity:
Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain of , ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative ...
Marc Malric (2012)
ESAIM: Probability and Statistics
Similarity:
The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
Marc Malric (2012)
ESAIM: Probability and Statistics
Similarity:
The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform...
Kouji Yano (2011)
ESAIM: Probability and Statistics
Similarity:
Wiener integral for the coordinate process is defined under the -finite measure unifying Brownian penalisations, which has been introduced by [Najnudel , 345 (2007) 459–466] and [Najnudel , 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, 258 (2010) 3492–3516] of Cameron-Martin formula for the -finite measure.
Alexei Bespalov, Norbert Heuer (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
In this paper we construct a new H(div)-conforming projection-based -interpolation operator that assumes only H() (div, )-regularity ( > 0) on the reference element (either triangle or square) . We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space (div, ), which is closely related...
Houman Owhadi, Lei Zhang, Leonid Berlyand (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ( ) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution ) minimizing...
Adrian J. Lew, Matteo Negri (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...
Adrian J. Lew, Matteo Negri (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...
A. Agouzal, K. Lipnikov, Yu. Vassilevsk (2010)
Mathematical Modelling of Natural Phenomena
Similarity:
We present a new method for generating a -dimensional simplicial mesh that minimizes the -norm, > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method
Nicolas Fournier (2011)
ESAIM: Probability and Statistics
Similarity:
We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some ∈ (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when neglecting...
Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)
ESAIM: Probability and Statistics
Similarity:
For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when ...