88 citations · 181 across the 17 of their papers we have counts for
17 papers
Hybridized Discontinuous Galerkin Methods for a Multiple Network Poroelasticity Model with Medical Applications
Johannes Kraus, Philip L. Lederer, Maria Lymbery +2
The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, th…
Robust approximation of generalized Biot-Brinkman problems
Q. Hong, J. Kraus, M. Kuchta +3
The generalized Biot-Brinkman equations describe the displacement, pressures and fluxes in an elastic medium permeated by multiple viscous fluid networks and can be used to study c…
A posteriori error estimates for domain decomposition methods
Johannes Kraus, Sergey Repin
Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and…
A new practical framework for the stability analysis of perturbed saddle-point problems and applications
Qingguo Hong, Johannes Kraus, Maria Lymbery +1
In this paper we prove a new abstract stability result for perturbed saddle-point problems based on a norm fitting technique. We derive the stability condition according to Babuska…
Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model
Johannes Kraus, Philip L. Lederer, Maria Lymbery +1
We consider the quasi-static Biot's consolidation model in a three-field formulation with the three unknown physical quantities of interest being the displacement …
Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot's consolidation and multiple-network poroelasticity models
Qingguo Hong, Johannes Kraus, Maria Lymbery +1
This work is concerned with the iterative solution of systems of quasi-static multiple-network poroelasticity (MPET) equations describing flow in elastic porous media that is perme…
Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems
Qingguo Hong, Johannes Kraus, Maria Lymbery +1
We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also refe…
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics
Johannes Kraus, Carl-Martin Pfeiler, Dirk Praetorius +2
The tangent plane scheme is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which describes the time evolution…
Conservative discretizations and parameter-robust preconditioners for Biot and multiple-network flux-based poroelastic models
Qinggou Hong, Johannes Kraus, Maria Lymbery +1
The parameters in the governing system of partial differential equations of multicompartmental poroelastic models typically vary over several orders of magnitude making its stable…
Reliable computer simulation methods for electrostatic biomolecular models based on the Poisson-Boltzmann equation
Johannes Kraus, Svetoslav Nakov, Sergey Repin
In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we…
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
Johannes Kraus, Svetoslav Nakov, Sergey Repin
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctn…
Parameter-robust stability of classical three-field formulation of Biot's consolidation model
Qingguo Hong, Johannes Kraus
This paper is devoted to the stability analysis of a classical three-field formulation of Biot's consolidation model where the unknown variables are the displacements, fluid flux (…
Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media
Johannes Kraus, Raytcho Lazarov, Maria Lymbery +2
In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het-…
Algebraic Multilevel Preconditioning in Isogeometric Analysis: Construction and Numerical Studies
K. P. S. Gahalaut, S. K. Tomar, J. K. Kraus
We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hie…
Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs
James Brannick, Yao Chen, Johannes Kraus +1
This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph…
A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
Blanca Ayuso de Dios, Ivan Georgiev, Johannes Kraus +1
We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace cor…
Polynomial of best uniform approximation to and smoothing in two-level methods
Johannes K. Kraus, Panayot S. Vassilevski, Ludmil T. Zikatanov
We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to on a finite interval with positive endpoints. As appli…