Zobrazeno 1 - 10
of 31
pro vyhledávání: '"SPREKELER, TIMO"'
We propose and rigorously analyze a finite element method for the approximation of stationary Fokker--Planck--Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients, and one wit
Externí odkaz:
http://arxiv.org/abs/2409.07371
We study the optimal rate of convergence in periodic homogenization of the viscous Hamilton-Jacobi equation $u^\varepsilon_t + H(\frac{x}{\varepsilon},Du^\varepsilon) = \varepsilon \Delta u^\varepsilon$ in $\mathbb R^n\times (0,\infty)$ subject to a
Externí odkaz:
http://arxiv.org/abs/2402.03091
Autor:
Sprekeler, Timo
Publikováno v:
SIAM J. Numer. Anal., 62 (2024), pp. 646-666
We study the homogenization of the equation $-A(\frac{\cdot}{\varepsilon}):D^2 u_{\varepsilon} = f$ posed in a bounded convex domain $\Omega\subset \mathbb{R}^n$ subject to a Dirichlet boundary condition and the numerical approximation of the corresp
Externí odkaz:
http://arxiv.org/abs/2305.19833
Publikováno v:
Comput. Methods Appl. Math., 24(3):649-672, 2024
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the methodology o
Externí odkaz:
http://arxiv.org/abs/2211.13731
We characterize diffusion matrices that yield a $L^{\infty}$ convergence rate of $\mathcal{O}(\varepsilon^2)$ in the theory of periodic homogenization of linear elliptic equations in nondivergence-form. Such type-$\varepsilon^2$ diffusion matrices ar
Externí odkaz:
http://arxiv.org/abs/2201.01974
Autor:
Kawecki, Ellya L., Sprekeler, Timo
Publikováno v:
ESAIM: M2AN 56 (2022) 679-704
In the first part of the paper, we study the discontinuous Galerkin (DG) and $C^0$ interior penalty ($C^0$-IP) finite element approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman--Isaacs (HJBI) e
Externí odkaz:
http://arxiv.org/abs/2104.14450
Publikováno v:
Multiscale Model. Simul. 19-2 (2021), pp. 1041-1065
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients satisfying
Externí odkaz:
http://arxiv.org/abs/2010.01647
Autor:
Sprekeler, Timo, Tran, Hung V.
Publikováno v:
Multiscale Model. Simul. 19-3 (2021), pp. 1453-1473
We study optimal convergence rates in the periodic homogenization of linear elliptic equations of the form $-A(x/\varepsilon):D^2 u^{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We show that the optimal rate for the conver
Externí odkaz:
http://arxiv.org/abs/2009.11259
Publikováno v:
ESAIM: M2AN 54 (2020) 1221-1257
We use uniform $W^{2,p}$ estimates to obtain corrector results for periodic homogenization problems of the form $A(x/\varepsilon):D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We propose and rigorously analyze a nume
Externí odkaz:
http://arxiv.org/abs/1905.11756
Publikováno v:
Computational Methods in Applied Mathematics; Jul2024, Vol. 24 Issue 3, p649-672, 24p