Results 1 to 10 of about 11,079 (89)
Approximation of high-dimensional parametric PDEs [PDF]
, 2015 Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even infinite.
Cohen, Albert, Devore, Ronald
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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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Second Order Backward Stochastic Differential Equations with Quadratic Growth [PDF]
, 2013 We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$ variable.
Possamaï, Dylan, Zhou, Chao
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Finite element methods for surface PDEs [PDF]
, 2013 In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the ...
Aragón +21 more
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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 ...
AV Knyazev +24 more
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Nonlinear Methods for Model Reduction
, 2020 The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the vector of ...
Bonito, Andrea +5 more
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MathematicsA model for the flow and thermal explosion of a micropolar gas is investigated, assuming the equation of state for a real gas. This model describes the dynamics of a gas mixture (fuel and oxidant) undergoing a one-step irreversible chemical reaction. The
Angela Bašić-Šiško
doaj +1 more source
A mixed $\ell_1$ regularization approach for sparse simultaneous approximation of parameterized PDEs
, 2018 We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs.
Dexter, Nick +2 more
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Ergodic Mean Field Games with H\"ormander diffusions [PDF]
, 2017 We prove existence of solutions for a class of systems of subelliptic PDEs arising from Mean Field Game systems with H\"ormander diffusion. These results are motivated by the feedback synthesis Mean Field Game solutions and the Nash equilibria of a large
Dragoni, Federica, Feleqi, Ermal
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Polynomial approximation via compressed sensing of high-dimensional functions on lower sets
, 2016 This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly decaying ...
Chkifa, Abdellah +3 more
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