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Journal Articles
- 2022
[j25]Stephan Gärttner
, Peter Frolkovic, Peter Knabner, Nadja Ray:
Efficiency of Micro-Macro Models for Reactive Two-Mineral Systems. Multiscale Model. Simul. 20(1): 433-461 (2022)- 2021
- [j24]Balthasar Reuter, Hennes Hajduk, Andreas Rupp, Florian Frank, Vadym Aizinger, Peter Knabner:
FESTUNG 1.0: Overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods. Comput. Math. Appl. 81: 3-41 (2021) - [j23]Stefan Metzger, Peter Knabner:
Homogenization of Two-Phase Flow in Porous Media From Pore to Darcy Scale: A Phase-Field Approach. Multiscale Model. Simul. 19(1): 320-343 (2021) - 2019
- [j22]Balthasar Reuter, Andreas Rupp, Vadym Aizinger, Peter Knabner:
Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems. Comput. Math. Appl. 77(9): 2291-2309 (2019) - 2018
- [j21]Alexander Jaust, Balthasar Reuter, Vadym Aizinger, Jochen Schütz, Peter Knabner:
FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation. Comput. Math. Appl. 75(12): 4505-4533 (2018) - [j20]Markus Gahn, Maria Neuss-Radu, Peter Knabner:
Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface. Networks Heterog. Media 13(4): 609-640 (2018) - 2017
- [j19]Raphael Schulz, Peter Knabner:
An Effective Model for Biofilm Growth Made by Chemotactical Bacteria in Evolving Porous Media. SIAM J. Appl. Math. 77(5): 1653-1677 (2017) - [j18]Joachim Hoffmann, Serge Kräutle, Peter Knabner:
Existence and Uniqueness of a Global Solution for Reactive Transport with Mineral Precipitation-Dissolution and Aquatic Reactions in Porous Media. SIAM J. Math. Anal. 49(6): 4812-4837 (2017) - 2016
- [j17]Balthasar Reuter, Vadym Aizinger, Manuel Wieland, Florian Frank, Peter Knabner:
FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part II: Advection operator and slope limiting. Comput. Math. Appl. 72(7): 1896-1925 (2016) - [j16]Markus Gahn, Maria Neuss-Radu, Peter Knabner:
Homogenization of Reaction-Diffusion Processes in a Two-Component Porous Medium with Nonlinear Flux Conditions at the Interface. SIAM J. Appl. Math. 76(5): 1819-1843 (2016) - [j15]Fabian Brunner, Julian Fischer, Peter Knabner:
Analysis of a Modified Second-Order Mixed Hybrid BDM1 Finite Element Method for Transport Problems in Divergence Form. SIAM J. Numer. Anal. 54(4): 2359-2378 (2016) - 2015
- [j14]Florian Frank, Balthasar Reuter, Vadym Aizinger, Peter Knabner:
FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part I: Diffusion operator. Comput. Math. Appl. 70(1): 11-46 (2015) - [j13]Nicolae Suciu, Florin A. Radu, S. Attinger, Lennart Schüler, Peter Knabner:
A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media. J. Comput. Appl. Math. 289: 241-252 (2015) - [j12]Nadja Ray, Tobias Elbinger, Peter Knabner:
Upscaling the Flow and Transport in an Evolving Porous Medium with General Interaction Potentials. SIAM J. Appl. Math. 75(5): 2170-2192 (2015) - 2014
- [j11]Fabian Brunner, Florin A. Radu, Peter Knabner:
Analysis of an Upwind-Mixed Hybrid Finite Element Method for Transport Problems. SIAM J. Numer. Anal. 52(1): 83-102 (2014) - 2013
- [j10]Nicolae Suciu, Florin A. Radu, Alexander Prechtel, Fabian Brunner, Peter Knabner:
A coupled finite element-global random walk approach to advection-dominated transport in porous media with random hydraulic conductivity. J. Comput. Appl. Math. 246: 27-37 (2013) - 2011
- [j9]Hannes Buchholzer, Christian Kanzow, Peter Knabner, Serge Kräutle:
The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions. Comput. Optim. Appl. 50(2): 193-221 (2011) - [j8]Florian Frank, Nadja Ray, Peter Knabner:
Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems. Comput. Vis. Sci. 14(8): 385-400 (2011) - 2010
- [j7]Markus Bause, Joachim Hoffmann, Peter Knabner:
First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods. Numerische Mathematik 116(1): 1-29 (2010) - [j6]Christof Eck, Baasansuren Jadamba, Peter Knabner:
Error Estimates for a Finite Element Discretization of a Phase Field Model for Mixtures. SIAM J. Numer. Anal. 47(6): 4429-4445 (2010) - 2008
- [j5]Florin A. Radu, Iuliu Sorin Pop, Peter Knabner:
Error estimates for a mixed finite element discretization of some degenerate parabolic equations. Numerische Mathematik 109(2): 285-311 (2008) - 2004
- [j4]Eckhard Schneid, Peter Knabner, Florin A. Radu:
A priori error estimates for a mixed finite element discretization of the Richards' equation. Numerische Mathematik 98(2): 353-370 (2004) - [j3]Florin A. Radu, Iuliu Sorin Pop, Peter Knabner:
Order of Convergence Estimates for an Euler Implicit, Mixed Finite Element Discretization of Richards' Equation. SIAM J. Numer. Anal. 42(4): 1452-1478 (2004) - 2002
- [j2]Markus Bause, Peter Knabner:
Uniform Error Analysis for Lagrange-Galerkin Approximations of Convection-Dominated Problems. SIAM J. Numer. Anal. 39(6): 1954-1984 (2002) - 2001
- [j1]Peter Knabner, Gerhard Summ:
The invertibility of the isoparametric mapping for pyramidal and prismatic finite elements. Numerische Mathematik 88(4): 661-681 (2001)
Informal and Other Publications
- 2023
- [i6]Lutz Angermann, Peter Knabner, Andreas Rupp:
Error estimates for completely discrete FEM in energy-type and weaker norms. CoRR abs/2301.06860 (2023) - 2019
- [i5]Cristian Daniel Alecsa, Imre Boros, Florian Frank, Peter Knabner, Mihai Nechita, Alexander Prechtel, Andreas Rupp, Nicolae Suciu:
Benchmark for numerical solutions of flow in heterogeneous groundwater formations. CoRR abs/1911.10774 (2019) - 2018
- [i4]Balthasar Reuter, Andreas Rupp, Vadym Aizinger, Florian Frank, Peter Knabner:
FESTUNG: A MATLAB /GNU Octave toolbox for the discontinuous Galerkin method. Part IV: Generic problem framework and model-coupling interface. CoRR abs/1806.03908 (2018) - 2016
- [i3]Balthasar Reuter, Vadym Aizinger, Manuel Wieland, Florian Frank, Peter Knabner:
FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting. CoRR abs/1602.05754 (2016) - 2014
- [i2]Peter Knabner, Jean Roberts:
Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture. CoRR abs/1401.0193 (2014) - [i1]Florian Frank, Balthasar Reuter, Vadym Aizinger, Peter Knabner:
FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator. CoRR abs/1408.3877 (2014)
Coauthor Index
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