Introduction to discrete functional analysis techniques for the numerical study of diffusion equations with irregular data [PDF]
, 2015 We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming non-physical regularity ...
Droniou, Jerome
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A forward--backward stochastic algorithm for quasi-linear PDEs [PDF]
, 2006 We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully coupled forward--backward SDEs, which provides an efficient probabilistic representation of this type of equation.
Delarue, François, Menozzi, Stéphane
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Error analysis of a space-time finite element method for solving PDEs on evolving surfaces [PDF]
, 2013 In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$.
Olshanskii, Maxim A., Reusken, Arnold
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Inertial manifolds and finite-dimensional reduction for dissipative PDEs [PDF]
, 2013 These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called Man\'e projection ...
Zelik, Sergey
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Stochastic PDEs with multiscale structure [PDF]
, 2012 We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise.
Hairer, Martin, Kelly, David
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Loss of regularity for Kolmogorov equations [PDF]
, 2015 The celebrated H\"{o}rmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic.
Hairer, Martin +2 more
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Solving linear parabolic rough partial differential equations [PDF]
, 2018 We study linear rough partial differential equations in the setting of [Friz and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear parabolic partial differential equation driven by a deterministic rough path $\mathbf{W}$ of H ...
Bayer, Christian +4 more
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Spatial smoothness of the stationary solutions of the 3D Navier--Stokes equations
, 2006 We consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deterministic and a random part.
Odasso, Cyril
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On ``hyperboloidal'' Cauchy data for vacuum Einstein equations and obstructions to smoothness of ``null infinity'' [PDF]
, 1993 Various works have suggested that the Bondi--Sachs--Penrose decay conditions on the gravitational field at null infinity are not generally representative of asymptotically flat space--times.
A. Trautman +16 more
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Local convergence of the FEM for the integral fractional Laplacian
, 2020 We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local $H^1$-norm and the localized energy norm.
Faustmann, Markus +2 more
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