179 citations · 613 across the 39 of their papers we have counts for
56 papers
Metric-driven numerical methods
Patrick Henning, Laura Huynh, Daniel Peterseim
In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on…
Hierarchical Super-Localized Orthogonal Decomposition Method
Jose C. Garay, Hannah Mohr, Daniel Peterseim +1
We present the construction of a sparse-compressed operator that approximates the solution operator of elliptic PDEs with rough coefficients. To derive the compressed operator, we…
Positivity preserving finite element method for the Gross-Pitaevskii ground state: discrete uniqueness and global convergence
Moritz Hauck, Yizhou Liang, Daniel Peterseim
We propose a positivity preserving finite element discretization for the nonlinear Gross-Pitaevskii eigenvalue problem. The method employs mass lumping techniques, which allow to t…
A Simple Collocation-Type Approach to Numerical Stochastic Homogenization
Moritz Hauck, Hannah Mohr, Daniel Peterseim
This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small…
Quantum Realization of the Finite Element Method
Matthias Deiml, Daniel Peterseim
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by -linear finite elements on Ca…
Mixed finite elements for the Gross-Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound
Dietmar Gallistl, Moritz Hauck, Yizhou Liang +1
We establish an a priori error analysis for the lowest-order Raviart-Thomas finite element discretisation of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence…