49 citations · 71 across the 8 of their papers we have counts for
9 papers
Well-Posedness and Finite Element Approximation of Mixed Dimensional Partial Differential Equations
Fredrik Hellman, Axel Målqvist, Malin Mosquera
We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of…
Numerical homogenization of spatial network models
Fredrik Edelvik, Morgan Görtz, Fredrik Hellman +2
We present and analyze a methodology for numerical homogenization of spatial networks, modelling e.g. diffusion processes and deformation of mechanical structures. The aim is to co…
Iterative solution of spatial network models by subspace decomposition
Morgan Görtz, Fredrik Hellman, Axel Målqvist
We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations…
Numerical upscaling for heterogeneous materials in fractured domains
Fredrik Hellman, Axel Målqvist, Siyang Wang
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured po…
Numerical upscaling of perturbed diffusion problems
Fredrik Hellman, Tim Keil, Axel Målqvist
In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We d…
Numerical homogenization of elliptic PDEs with similar coefficients
Fredrik Hellman, Axel Målqvist
We consider a sequence of elliptic partial differential equations (PDEs) with different but similar rapidly varying coefficients. Such sequences appear, for example, in splitting s…
Contrast independent localization of multiscale problems
Fredrik Hellman, Axel Målqvist
The accuracy of many multiscale methods based on localized computations suffers from high contrast coefficients since the localization error generally depends on the contrast. We s…
Multiscale mixed finite elements
Fredrik Hellman, Patrick Henning, Axel Målqvist
In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element…
A multilevel Monte Carlo method for computing failure probabilities
Daniel Elfverson, Fredrik Hellman, Axel Målqvist
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs wh…