Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs [PDF]
Journal of Differential Equations, 2015 48 ...
Irina Kmit, Lutz Recke
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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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Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge--Kutta methods for Hamiltonian semilinear evolution equations [PDF]
, 2015 We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic initial data ...
Oliver, Marcel, Wulff, Claudia
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Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model [PDF]
, 2015 Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3D Navier--Stokes equations, for certain initial data for which ...
Blömker, Dirk +2 more
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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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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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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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Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems [PDF]
, 2016 In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in
Kuo, Frances Y. +4 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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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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