Books

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

2019

Author(s) Title Source Links
Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems. Computers & Mathematics with Applications. (2019) 77 (9) 2291-2309. [doi] [www] [BibTex]

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) 124 (3) 803-824. [doi] [www] [BibTex]
A Local Discontinuous Galerkin Scheme for Darcy Flow with Internal Jumps. Computational Geosciences. (2018) 22 (4) 1149-1159. [doi] [www] [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) 75 (12) 4505-4533. [doi] [www] [BibTex]
FESTUNG: A MATLAB /GNU Octave toolbox for the discontinuous Galerkin method. Part IV: Generic problem framework and model-coupling interface. preprint. (2018) [www] [BibTex]
Wavelet-based priors accelerate maximum-a-posteriori optimization in Bayesian inverse problems. Methodology and computing in applied probability. (2018) submitted. [BibTex]
Microaggregates in Soils. Journal of Plant Nutrition and Soil Science. (2018) 181 104-136. [doi] [www] [BibTex]
Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the bulk-layer interface. Networks & Heterogeneous Media. (2018) 13 (4) 609-640. [doi] [www] [BibTex]
A global implicit solver for miscible reactive multiphase multicomponent flow in porous media. Computational Geosciences. (2018) 1-22. [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]

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]

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