Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness

Autor: Bénédicte Puig, Isabelle Greff, Helmut Harbrecht, Marc Dambrine
Přispěvatelé: Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2017
Předmět:
Physics and Astronomy (miscellaneous)
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
010103 numerical & computational mathematics
Boundary layer thickness
01 natural sciences
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
Neumann boundary condition
Free boundary problem
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Boundary value problem
[MATH]Mathematics [math]
0101 mathematics
Mathematics
Numerical Analysis
Applied Mathematics
Mathematical analysis
Mixed boundary condition
Robin boundary condition
Computer Science Applications
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
010101 applied mathematics
Thin layer equation
Computational Mathematics
Modeling and Simulation
Blasius boundary layer
Cauchy boundary condition
Random domain
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2017, 330, pp.943--959. ⟨10.1016/j.jcp.2016.10.044⟩
ISSN: 0021-9991
1090-2716
Popis: ACL; International audience; The present article is dedicated to the numerical solution of homogeneous Neumann boundary value problems on domains with a thin layer of different conductivity and of random thickness. By changing the boundary condition, the boundary value problem given on the random domain can be transformed into a boundary value problem on a fixed domain. The randomness is then contained in the coefficients of the new boundary condition. This thin coating can be expressed by a random Ventcell boundary condition and yields a second order accurate solution in the scale parameter epsilon of the layer's thickness. With the help of the Karhunen-Loeve expansion, we transform this random boundary value problem into a deterministic, parametric one with a possibly high-dimensional parameter y. Based on the decay of the random fluctuations of the layer's thickness, we prove rates of decay of the derivatives of the random solution with respect to this parameter y which are robust in the scale parameter epsilon. Numerical results validate our theoretical findings.
Databáze: OpenAIRE
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