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Träfflista för sökning "L773:9783319964140 OR L773:9783319964157 "

Sökning: L773:9783319964140 OR L773:9783319964157

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1.
  • Burman, Erik N., et al. (författare)
  • A cut finite element method with boundary value correction for the incompressible Stokes equations
  • 2019
  • Ingår i: Numerical mathematics and advanced applications ENUMATH 2017. - Cham : Springer. - 9783319964140 - 9783319964157 ; , s. 183-192
  • Konferensbidrag (refereegranskat)abstract
    • We design a cut finite element method for the incompressible Stokes equations on domains with curved boundary. The cut finite element method allows for the domain boundary to cut through the elements of the computational mesh in a very general fashion. To further facilitate the implementation we propose to use a piecewise affine discrete domain even if the physical domain has curved boundary. Dirichlet boundary conditions are imposed using Nitsche’s method on the discrete boundary and the effect of the curved physical boundary is accounted for using the boundary value correction technique introduced for cut finite element methods in Burman et al. (Math Comput 87(310):633–657, 2018). 
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2.
  • Wahlsten, Markus, 1986-, et al. (författare)
  • Galerkin projection and numerical integration for a stochastic investigation of the viscous Burgers equation : An initial attempt
  • 2019
  • Ingår i: Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. - Cham : Springer. - 9783319964140 - 9783319964157 ; , s. 1005-1013
  • Bokkapitel (refereegranskat)abstract
    • We consider a stochastic analysis of the non-linear viscous Burgers’ equation and focus on the comparison between intrusive and non-intrusive uncertainty quantification methods. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are applied to a provably stable formulation of the viscous Burgers’ equation, and compared. As measures of comparison: variance size, computational efficiency and accuracy are used.
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3.
  • Koskela, Antti, et al. (författare)
  • On a generalization of neumann series of bessel functions using Hessenberg matrices and matrix exponentials
  • 2019
  • Ingår i: European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017. - Cham : Springer. - 9783319964140 ; , s. 205-214
  • Konferensbidrag (refereegranskat)abstract
    • The Neumann expansion of Bessel functions (of integer order) of a function g: ℂ→ ℂ corresponds to representing g as a linear combination of basis functions φ0, φ1, …, i.e., g(s)=∑ℓ=0 ∞wℓφℓ(s), where φi(s) = Ji(s), i = 0, …, are the Bessel functions. In this work, we study an expansion for a more general class of basis functions. More precisely, we assume that the basis functions satisfy an infinite dimensional linear ordinary differential equation associated with a Hessenberg matrix, motivated by the fact that these basis functions occur in certain iterative methods. A procedure to compute the basis functions as well as the coefficients is proposed. Theoretical properties of the expansion are studied. We illustrate that non-standard basis functions can give faster convergence than the Bessel functions.
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  • Resultat 1-3 av 3

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