Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps [PDF]
, 2013 Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities ...
Dolean Maini, Victorita +5 more
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An algorithmic construction of a priori estimates for nonlinear higher-order PDEs
, 2007 An algorithmic construction of a priori estimates for nonlinear higher-order PDEsAn algorithmic construction of a priori estimates for nonlinear higher-order ...
Jüngel, Ansgar
core +9 more sources
Epistemic Norms, A Priority, and Self-Knowledge [PDF]
, 2011 This thesis is primarily focussed on developing a novel characterisation of the distinction between a priori and a posteriori justification. My working hypothesis is that we can make a surprising amount of progress in this field by paying attention to ...
Flockemann, Richard
core +6 more sources
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.
Martin Hairer +3 more
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Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice [PDF]
, 2013 We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3):905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of ...
Ortner, C. +2 more
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Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes [PDF]
, 2010 A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the ...
Rüdiger Müller +11 more
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A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D [PDF]
, 2010 For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented.
Christoph Ortner, Ortner, Christoph
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A priori estimates for rough PDEs with application to rough conservation laws [PDF]
, 2019 International audienceWe introduce a general framework to study PDEs driven by rough paths: we develop new a priori estimates based on a rough Gronwall lemma argument for weak solutions to rough PDEs.
Hofmanova, Martina +3 more
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A priori error estimates for energy-based quasicontinuum approximations of a periodic chain [PDF]
, 2011 We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasi-nonlocal QC method.
Christoph Ortner +3 more
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A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient [PDF]
, 2010 summary:We derive local a priori estimates of the Hölder norm of solutions to quasilinear elliptic systems with quadratic nonlinearities in the gradient.
Arkhipova, Arina A., Stará, Jana
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