Books

A list of all published books by Peter Knabner can be found here.

2018

Author(s) Title Source Links
Analysis of a mixed discontinuous Galerkin method for instationary Darcy flow. Computational Geosciences. (2018) 22 (1) 179-194. [doi] [www] [BibTex]
Old and new approaches predicting the diffusion in porous media. Transport in Porous Media. (2018) submitted. [BibTex]
FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation. Computers and Mathematics with Applications. (2018) [doi] [www] [BibTex]

2017

Author(s) Title Source Links
Strong solvability up to clogging of an effective diffusion-precipitation model in an evolving porous medium. European Journal of Applied Mathematics. (2017) 28 (2) 179-207. [doi] [www] [BibTex]
Upscaling of a system of diffusion-reaction equations coupled with a system of ordinary differential equations originating in the context of crystal dissolution and precipitation of minerales in a porous medium. Advances in Mathematical Sciences and Applications. (2017) 26 (1) 39-81. [BibTex]
Derivation of an effective model for metabolic processes in living cells including substrate channeling. Vietnam Journal of Mathematics. (2017) 45 (1-2) 265-293. [doi] [BibTex]
Convergence analysis of a BDF2 / mixed finite element discretization of a Darcy-Nernst-Planck-Poisson system. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). (2017) accepted. [doi] [BibTex]
Derivation and Analysis of an Effective Model for Biofilm Growth in Evolving Porous Media. Mathematical Methods in the Applied Sciences. (2017) 40 (8) 2930–2948 . [doi] [BibTex]
An effective model for biofilm growth made by chemotactical bacteria in evolving porous media. SIAM J. Appl. Math.. (2017) 77 (5) 1653–1677. [doi] [BibTex]
Convergence Order Estimates of the Local Discontinuous Galerkin Method for Instationary Darcy Flow. Numerical Methods for Partial Differential Equations. (2017) 33 (4) 1374–1394 . [doi] [BibTex]
Existence and uniqueness of a global solution for reactive transport with mineral precipitation-dissolution and aquatic reactions in porous media. SIAM Journal on Mathematical Analysis. (2017) 49 (6) 4812–4837. [doi] [BibTex]
A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity. Vietnam Journal of Mathematics. (2017) 45 (1) 179–198. [doi] [BibTex]
A numerical study of Haar wavelet priors in an elliptical Bayesian inverse problem. SIAM Journal on Scientific Computing (SISC). (2017) submitted. arXiv:1710.07428. [www] [BibTex]
A Local Discontinuous Galerkin Scheme for Darcy Flow with Internal Jumps. Computational Geosciences. (2017) submitted . [BibTex]

2016

Author(s) Title Source Links
Homogenization of reaction-diffusion processes in a two-component porous medium with nonlinear flux conditions at the interface. SIAM Journal on Applied Mathematics. (2016) 76 (5) 1819-1843. [doi] [BibTex]
Analysis of a modified second-order mixed hybrid BDM₁ finite Element method for transport problems in divergence form. SIAM Journal on Numerical Analysis. (2016) 54 (4) 2359–2378. [doi] [www] [BibTex]
Model based design of biochemical micro-reactors. Frontiers in Bioengineering and Biotechnology. (2016) 4 (13) [doi] [www] [BibTex]
Towards a filtered density function approach for reactive transport in groundwater. Advances in Water Resources. (2016) 90 83-98. [doi] [BibTex]
A thermodynamically consistent model for multicomponent electrolyte solutions. Preprint-Reihe Angewandte Mathematik des Departments Mathematik der Friedrich-Alexander-Universität Erlangen-Nürnberg. (2016) (383) S. 1–45 (arXiv:1605.07455). [www] [BibTex]
Global existence of weak solutions of a model for electrolyte solutions - Part 1: Two-component case. Preprint-Reihe Angewandte Mathematik des Departments Mathematik der Friedrich-Alexander-Universität Erlangen-Nürnberg. (2016) (380) S. 1–26 (arXiv:1605.07396). [www] [BibTex]
Global existence of weak solutions of a model for electrolyte solutions - Part 2: Multicomponent case. Preprint-Reihe Angewandte Mathematik des Departments Mathematik der Friedrich-Alexander-Universität Erlangen-Nürnberg. (2016) (381) S. 1–15 (arXiv:1605.07445). [www] [BibTex]
FESTUNG: A MATLAB /GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting. Computers and Mathematics with Applications. (2016) 72 (7) 1896-1925. [doi] [www] [BibTex]
Modeling and simulation of coagulation according to DLVO-theory in a continuum model for electrolyte solutions. Preprint-Reihe Angewandte Mathematik des Departments Mathematik der Friedrich-Alexander-Universität Erlangen-Nürnberg. (2016) (382) S. 1–14 (arXiv:1605.08602). [www] [BibTex]
Including van der Waals Forces in Diffusion-Convection Equations - Modeling, Analysis, and Numerical Simulations. Preprint-Reihe Angewandte Mathematik des Departments Mathematik der Friedrich-Alexander-Universität Erlangen-Nürnberg. (2016) (373) S. 1–15 (arXiv:1608.08431). [www] [BibTex]
Efficient Realization of the mixed fintite elment discretization for nonlinear problems. Manuscript. (2016) arXiv:1610.05528. [BibTex]
Sovability of the mixed Formulation for Darcy-Forchheimer Flow in Porous Media. (2016) arXiv:1608.08829. [BibTex]
A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers. Advances in Water Resources. (2016) 96 55-67. [doi] [BibTex]
Hybrid Discretization Methods for Transient Numerical Simulation of Combustion in Porous Media. Submitted for publication. (2016) arXiv:1608.08817. [BibTex]

2015

Author(s) Title Source Links
Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition. Advances in Water Resources. (2015) 86 (A) 209–216. [doi] [BibTex]
Upscaling flow and transport in an evolving porous medium with general interaction potentials. SIAM Journal on Applied Mathematics. (2015) 75 (5) 2170–2192. [doi] [www] [BibTex]

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