This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution-free ......

This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal ...

We present and analyze a pollution-free Petrov-Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ as a variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard continuous ......

A stable splitting of 2m-th order elliptic partial differential equations into 2(m−1) problems of Poisson type and one generalized Stokes problem is established for any space dimension d ≥ 2 and any integer m ≥ 1. This ......

This paper gives a re-interpretation of the multiscale method of Målqvist and Peterseim [Math. Comp. 2014] by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the ...

This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios ^λ_k/λ_k of the kth numerical eigenvalue ^λ_k ......