Peter Knabner

Publication Activity (10 Years)

Years Active: 2001-2023
Publications (10 Years): 15

Top Topics

Diffusion Processes

Computationally Efficient

Top Venues

Comput. Math. Appl.

SIAM J. Appl. Math.

SIAM J. Numer. Anal.

Publications

Lutz Angermann, Peter Knabner, Andreas Rupp
Error estimates for completely discrete FEM in energy-type and weaker norms. CoRR (2023)
Stephan Gärttner, Peter Frolkovic, Peter Knabner, Nadja Ray
Efficiency of Micro-Macro Models for Reactive Two-Mineral Systems. Multiscale Model. Simul. 20 (1) (2022)
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) (2021)
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 (2021)
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) (2019)
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 (2019)
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) (2018)
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) (2018)
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 (2018)
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) (2017)
Raphael Schulz, Peter Knabner
An Effective Model for Biofilm Growth Made by Chemotactical Bacteria in Evolving Porous Media. SIAM J. Appl. Math. 77 (5) (2017)
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) (2016)
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 (2016)
Fabian Brunner, Julian Fischer, Peter Knabner
Finite Element Method for Transport Problems in Divergence Form. SIAM J. Numer. Anal. 54 (4) (2016)
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) (2016)
Nicolae Suciu, Florin A. Radu, S. Attinger, L. Schüler, Peter Knabner
A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media. J. Comput. Appl. Math. 289 (2015)
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) (2015)
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) (2015)
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) (2014)
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 (2014)
Florian Frank, Balthasar Reuter, Vadym Aizinger, Peter Knabner
FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator. CoRR (2014)
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 (2013)
Florian Frank, Nadja Ray, Peter Knabner
Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems. Comput. Vis. Sci. 14 (8) (2011)
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) (2011)
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) (2010)
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) (2010)
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) (2008)
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) (2004)
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) (2004)
Markus Bause, Peter Knabner
Uniform Error Analysis for Lagrange-Galerkin Approximations of Convection-Dominated Problems. SIAM J. Numer. Anal. 39 (6) (2002)
Peter Knabner, Gerhard Summ
The invertibility of the isoparametric mapping for pyramidal and prismatic finite elements. Numerische Mathematik 88 (4) (2001)