15 citations · 64 across the 14 of their papers we have counts for
16 papers
Analytical and numerical periodic homogenization of Hamilton--Jacobi--Bellman and Isaacs equations in a Cordes framework
Timo Sprekeler, Hung V. Tran
We study periodic homogenization of fully-nonlinear second-order Hamilton--Jacobi--Bellman and Isaacs equations subject to a homogeneous Dirichlet boundary condition and the numeri…
Revisiting Picard's proof of the Picard--Weber--Weck selection theorem
Yi-Sheng Lim, Timo Sprekeler, Marcus Waurick
Revisiting the rationale provided by Picard in the seminal paper [13], we provide an independent, self-contained proof of the Maxwell compactness property for weak Lipschitz domain…
A post-processed higher-order multiscale method for nondivergence-form elliptic equations
Moritz Hauck, Roland Maier, Timo Sprekeler
We study the finite element approximation of linear second-order elliptic partial differential equations in nondivergence form with highly heterogeneous diffusion and drift coeffic…
A Cordes framework for stationary Fokker--Planck--Kolmogorov equations
Timo Sprekeler
We first review the Cordes condition for nondivergence-form differential operators through the lens of Campanato's theory of near operators. We then survey a recently proposed Cord…
Homogenization of non-divergence form operators in i.i.d. random environments
Xiaoqin Guo, Timo Sprekeler, Hung V. Tran
We study random walks in a balanced, i.i.d. random environment in for . We establish improved convergence rates for the homogenization of the Dirichlet probl…
Numerical approximation of effective diffusivities in homogenization of nondivergence-form equations with large drift by a Lagrangian method
Timo Sprekeler, Han Wu, Zhiwen Zhang
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drif…
Stable localized orthogonal decomposition in Raviart-Thomas spaces
Patrick Henning, Hao Li, Timo Sprekeler
This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based…
Finite element approximation of stationary Fokker--Planck--Kolmogorov equations with application to periodic numerical homogenization
Timo Sprekeler, Endre Süli, Zhiwen Zhang
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…
Optimal rate of convergence in periodic homogenization of viscous Hamilton-Jacobi equations
Jianliang Qian, Timo Sprekeler, Hung V. Tran +1
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…
Homogenization of nondivergence-form elliptic equations with discontinuous coefficients and finite element approximation of the homogenized problem
Timo Sprekeler
We study the homogenization of the equation posed in a bounded convex domain subject to a Dirichlet…
Computational multiscale methods for nondivergence-form elliptic partial differential equations
Philip Freese, Dietmar Gallistl, Daniel Peterseim +1
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients sat…
Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form
Xiaoqin Guo, Timo Sprekeler, Hung V. Tran
We characterize diffusion matrices that yield a convergence rate of in the theory of periodic homogenization of linear elliptic equations…
Discontinuous Galerkin and -IP finite element approximation of periodic Hamilton--Jacobi--Bellman--Isaacs problems with application to numerical homogenization
Ellya L. Kawecki, Timo Sprekeler
In the first part of the paper, we study the discontinuous Galerkin (DG) and interior penalty (-IP) finite element approximation of the periodic strong solution to the f…
Optimal convergence rates for elliptic homogenization problems in nondivergence-form: analysis and numerical illustrations
Timo Sprekeler, Hung V. Tran
We study optimal convergence rates in the periodic homogenization of linear elliptic equations of the form subject to a homogeneous Diri…
Mixed finite element approximation of periodic Hamilton--Jacobi--Bellman problems with application to numerical homogenization
Dietmar Gallistl, Timo Sprekeler, Endre Süli
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-…
Finite Element Approximation of Elliptic Homogenization Problems in Nondivergence-Form
Yves Capdeboscq, Timo Sprekeler, Endre Süli
We use uniform estimates to obtain corrector results for periodic homogenization problems of the form subject to a homogeneous…