13 citations · 28 across the 18 of their papers we have counts for
22 papers
A Hybridizable Discontinuous Galerkin Method for Wave Propagation in Elastic Beam Networks
Moritz Hauck, Joseph Holten, Axel Målqvist +2
This paper studies the numerical solution of elastic wave propagation on networks, modeled by elastodynamic equations posed on each edge, coupled at the nodes through suitable tran…
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…
Numerical Simulation of Beam Network Models
Morgan Görtz, Moritz Hauck, Axel Målqvist +2
Network models are used as efficient representation of materials with complex, interconnected locally one-dimensional structures. They typically accurately capture the mechanical p…
A High-Order Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems
Moritz Hauck, Alexei Lozinski
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes…
A Localized Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems
Moritz Hauck, Axel Målqvist, Malin Mosquera
We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The m…
Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods
Christian Alber, Peter Bastian, Moritz Hauck +1
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approxim…
A Hybrid High-Order Method for the Gross--Pitaevskii Eigenvalue Problem
Moritz Hauck, Yizhou Liang
We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the groun…
A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods
Moritz Hauck, Alexei Lozinski, Roland Maier
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we a…
A Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems
Moritz Hauck, Alexei Lozinski
In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the Localized Orthogonal Decomposition (LOD) methodology and has approximati…
Arbitrary order approximations at constant cost for Timoshenko beam network models
Moritz Hauck, Axel Målqvist, Andreas Rupp
This paper considers the numerical solution of Timoshenko beam network models, comprised of Timoshenko beam equations on each edge of the network, which are coupled at the nodes of…
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…
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…
An algebraic multiscale method for spatial network models
Moritz Hauck, Roland Maier, Axel Målqvist
In this work, we present a multiscale approach for the reliable coarse-scale approximation of spatial network models represented by a linear system of equations with respect to the…
A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems
Francesca Bonizzoni, Moritz Hauck, Daniel Peterseim
This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varyi…
A Super-Localized Generalized Finite Element Method
Philip Freese, Moritz Hauck, Tim Keil +1
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the metho…
An improved high-order method for elliptic multiscale problems
Zhaonan Dong, Moritz Hauck, Roland Maier
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are…
Super-localization of spatial network models
Moritz Hauck, Axel Målqvist
Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore…
Super-localized Orthogonal Decomposition for high-frequency Helmholtz problems
Philip Freese, Moritz Hauck, Daniel Peterseim
We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber . On a coarse mesh…
Super-localization of elliptic multiscale problems
Moritz Hauck, Daniel Peterseim
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a …
Multi-resolution Localized Orthogonal Decomposition for Helmholtz problems
Moritz Hauck, Daniel Peterseim
We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The met…
A subcell-enriched Galerkin method for advection problems
Andreas Rupp, Moritz Hauck, Vadym Aizinger
In this work, we introduce a generalization of the enriched Galerkin (EG) method. The key feature of our scheme is an adaptive two-mesh approach that, in addition to the standard e…