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Themengebiete:

Nichtlineare Evolutionsgleichungen zweiter Ordnung

E. Emmrich and D. Šiška
Nonlinear stochastic evolution equations of second order with damping
Stochastics and Partial Differential Equations: Analysis and Computations 5 (2017) 1, pp. 81-112
(link to journal) (PDF)

E. Emmrich, D. Šiška, and Wróblewska-Kamińska
Equations of second order in time with quasilinear damping: existence in Orlicz spaces via convergence of a full discretisation
Mathematical Methods in the Applied Sciences 39 (2016) 10, pp. 2449-2460
(link to journal) (PDF)

D. Puhst
On the evolutionary fractional p-Laplacian
Appl. Math. Res. Express 2015, 2, pp. 253-273
(link to journal) (preliminary version as PDF)

E. Emmrich, D. Šiška, and M. Thalhammer
On a full discretisation for nonlinear second-order evolution equations with monotone damping: construction, convergence and error estimates
Found. Comput. Math. 15 (2015) 6, pp. 1653-1701
(link to journal) (PDF)

E. Emmrich and D. Šiška
Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization
J. Differential Equations 255 (2013) 10, pp. 3719-3746 
(link to journal) (preliminary version as PDF)

E. Emmrich and D. Šiška
Full discretization of second-order nonlinear evolution equations: strong convergence and applications
Comput. Methods Appl. Math. 11 (2011) 4, pp. 441-459
(link to journal) (preliminary version as PDF) (PDF, 571,0 KB)

E. Emmrich and M. Thalhammer
Doubly nonlinear evolution equations of second order: Existence and fully discrete approximation
J. Differential Equations 251 (2011) 1, pp. 82-118
(link to journal) (preliminary version as PDF) (PDF, 240,7 KB)

E. Emmrich and M. Thalhammer
Convergence of a time discretisation for doubly nonlinear evolution equations of second order
Found. Comput. Math. 10 (2010) 2, pp. 171-190
(link to journal) (preliminary version as PDF) (PDF, 222,5 KB)

Nichtlineare Evolutionsgleichungen erster Ordnung

A. Eikmeier, E. Emmrich
On a multivalued differential equation with nonlocality in time
(submitted)
(arxiv version)

M. Eisenmann, E. Emmrich, and V. Mehrmann
Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data 
Evolution Equations & Control Theory 8 (2019) 2, pp. 315-342
(link to journal) (arxiv version)

A. Eikmeier, E. Emmrich, and H.-C. Kreusler
Nonlinear evolution equations with exponentially decaying memory: Existence via time discretisation, uniqueness, and stability
Comput. Methods Appl. Math. (2018, published online)
(link to journal) (arXiv version)

W.-J. Beyn, E. Emmrich, and J. Rieger
Semilinear parabolic differential inclusions with one-sided Lipschitz nonlinearities
Journal of Evolution Equations 18 (2018)  3, pp. 1319–1339
(link to journal) (preliminary version as PDF)

A. Bacho, E. Emmrich, and A. Mielke
An existence result and evolutionary Γ-convergence for perturbed gradient systems
Journal of Evolution Equations (2018, accepted for publication)
(link to journal) (arxiv version)

M. Eisenmann, R. Kruse, M. Kovacs, and S. Larsson
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients (2017)
(arxiv version) 

M. Eisenmann and E. Hansen
Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations (2017)
(arXiv version) 

E. Emmrich and G. Vallet
On a nonlinear abstract Volterra equation
Journal of Integral Equations and Applications 28 (2016) 1, pp. 75-89
(link to journal) (preliminary version as PDF)

M. Bukal, E. Emmrich, and A. Jüngel
Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation
Numer. Math. 127 (2014) 2, pp. 365-396
(link to journal) (preliminary version as PDF)

E. Emmrich and A. Wróblewska
Convergence of a full discretization of quasilinear parabolic equations in isotropic and anisotropic Orlicz spaces
SIAM J. Numer. Anal. 51 (2013) 2, pp. 1163-1184
(link to journal) (preliminary version as PDF)

E. Emmrich and G. Vallet
Existence via time discretization for a class of doubly nonlinear operator-differential equations of Barenblatt-type
J. Differential Equations 254 (2013) 6, pp. 2499-2514
(link to journal) (preliminary version as PDF)

E. Emmrich
Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin method
BIT Numer. Math. 51 (2011) 3, pp. 581-607
(link to journal) (preliminary version as PDF) (PDF, 226,2 KB)

E. Emmrich and M. Thalhammer
Stiffly accurate Runge-Kutta methods for nonlinear evolution problems governed by a monotone operator
Math. Comp. 79 (2010), pp. 785-806
(link to journal) (preliminary version as PDF) (PDF, 306,0 KB)

E. Emmrich
Variable time-step θ-scheme for nonlinear evolution equations governed by a monotone operator
Calcolo 46 (2009) 3, pp. 187-210 
(link to journal) (preliminary version as PDF) (PDF, 268,8 KB)

E. Emmrich
Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator
BIT Numer. Math. 49 (2009), pp. 297-323
(link to journal) (preliminary version as PDF) (PDF, 273,0 KB)

E. Emmrich
Two-step BDF time discretisation of nonlinear evolution problems governed by monotone operators with strongly continuous perturbations
Comput. Methods Appl. Math. 9 (2009) 1, pp. 37-62
(link to journal) (PDF) (PDF, 290,4 KB)

E. Emmrich
Stability and error of the variable two-step BDF for semilinear parabolic problems
J. Appl. Math. & Computing 19 (2005) 1-2, pp. 33-55
(link to journal) (PDF) (PDF, 250,3 KB)

E. Emmrich
Quantitative error estimates for the implicit Euler scheme for linear evolutionary problems with rough data
Preprint No. 671, Fachbereich Mathematik, TU Berlin, March 2000.
(PDF) (PDF, 276,0 KB)

E. Emmrich
Discrete versions of Gronwall's lemma and their application to the numerical analysis of parabolic problems
Preprint No. 637, Fachbereich Mathematik, TU Berlin, July 1999.
(PDF) (PDF, 417,1 KB)

E. Emmrich
Zeitdiskretisierung parabolischer Probleme und Fehlerabschätzungen unter verschiedenen Regularitätsannahmen
In: Preprint MBI-98-1, Universität Magdeburg, Dezember 1997.

Gleichungen aus der Elastizitätstheorie und Peridynamik

E. Emmrich and D. Puhst
A short note on modeling damage in peridynamics
J. Elasticity 123 (2016) 2, pp. 245–252
(link to journal) (preliminary version as PDF)

E. Emmrich and D. Puhst
Survey of existence results in nonlinear peridynamics in comparison with local elastodynamics 
Comput. Methods Appl. Math. 15 (2015) 4, pp. 483–496
(link to journal) (PDF)

E. Emmrich and D. Puhst
Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics
Nonlinearity 28 (2015) 1, pp. 285–307 
(link to journal) (preliminary version as PDF)

E. Emmrich and D. Puhst
Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function
Commun. Math. Sci. 11 (2013) 4, pp. 1039–1049
(link to journal) (preliminary version as PDF)

E. Emmrich, R. B. Lehoucq, and D. Puhst
Peridynamics: a nonlocal continuum theory
In: M. Griebel and M. A. Schweitzer (eds.),
Meshfree Methods for Partial Differential Equations VI,
Lect. N. Comput. Sci. Engin., Vol. 89, 2013, pp. 45–65
(link to article) (preliminary version as PDF)

E. Emmrich and M. Thalhammer
A class of integro-differential equations incorporating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: Existence via time discretisation
Nonlinearity 24 (2011), pp. 2523–2546
(link to journal) (preliminary version as PDF) (PDF, 394,7 KB)

E. Emmrich and O. Weckner
On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity
Commun. Math. Sci. 5 (2007) 4, pp. 851–864 
(link to journal) (preliminary version as PDF) (PDF, 193,7 KB)

E. Emmrich and O. Weckner
Analysis and numerical approximation of an integro-differential equation modelling non-local effects in linear elasticity
Math. Mech. Solids 12 (2007) 4, pp. 363–384
(link to journal) (preliminary version as PDF) (PDF, 337,2 KB)

E. Emmrich and O. Weckner
The peridynamic equation and its spatial discretisation
Math. Model. Anal. 12 (2007) 1, pp. 17–27
(link to journal) (PDF) (PDF, 737,6 KB)

E. Emmrich and O. Weckner
The peridynamic equation of motion in non-local elasticity theory
In: C. A. Mota Soares et al. (eds.), III European Conference on Computational Mechanics. Solids, Structures and Coupled Problems in Engineering (Lisbon, June 2006), Springer, 2006, 19 p. 
(link to proceedings) (preliminary version as PDF) (PDF, 701,0 KB)

E. Emmrich and O. Weckner
Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar 
J. Comput. Appl. Mech. 6 (2005) 2, pp. 311–319
(link to journal) (PDF)

E. Emmrich and O. Weckner
The peridynamic model in non-local elasticity theory
PAMM 6 (2006) 1, pp. 155–156
(link to journal)

Gleichungen aus der Strömungsmechanik

E. Emmrich and R. Lasarzik 
Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations (2018)
accepted for publication in IMA Journal of Applied Mathematics
(link to journal) (preliminary version as PDF)

R. Lasarzik
Measure-valued solutions to the Ericksen–Leslie model equipped with the Oseen–Frank energy
Nonlinear Analysis 179 (2019), pp. 146-183
(link to journal) (arxiv version)

E. Emmrich and R. Lasarzik
Existence of weak solutions to the Ericksen–Leslie model for a general class of free energies
Math. Methods Appl. Sci. 41 (2018), pp. 6492-6518
(link to journal) (arxiv version)

R. Lasarzik
Weak-strong uniqueness for measure-valued solutions to the Ericksen–Leslie model equipped with the Oseen–Frank free energy
J. Math. Anal. Appl. (2018, accepted for publication)
(link to journal) (arxiv version)

E. Emmrich, S. H. L. Klapp, and R. Lasarzik
Nonstationary models for liquid crystals: A fresh mathematical perspective
Journal of Non-Newton. Fluid Mech. 259 (2018), pp. 32-47
(link to journal) (PDF) 

E. Emmrich and R. Lasarzik
Weak-strong uniqueness for the general Ericksen–Leslie system in three dimensions
Discrete Contin. Dyn. Syst. 38 (2018) 9, pp. 4617-4635
(link to journal) (arxiv version) 

E. Emmrich and V. Mehrmann
Operator Differential-Algebraic Equations arising in Fluid Dynamics
Comput. Methods Appl. Math. 13 (2013) 4,  pp. 443-470
(link to journal)

E. Emmrich and V. Mehrmann 
Analysis of operator differential-algebraic equations arising in fluid dynamics. Part II. The infinite dimensional case 
Preprint 2013-28, Institut für Mathematik, Technische Universität Berlin, August 2013, 24p.
(preliminary version as PDF)

E. Emmrich and V. Mehrmann
Analysis of operator differential-algebraic equations arising in fluid dynamics. Part I. The finite dimensional case
Preprint 12-2010, Institut für Mathematik, Technische Universität Berlin, May 2010, 15p.
(preliminary version as PDF) (PDF, 288,5 KB)

E. Emmrich and D. Šiška
Full discretization of the porous medium/fast diffusion equation based on its very weak formulation
Commun. Math. Sci. 10 (2012) 4, pp. 1055-1080
(link to journal) (preliminary version as PDF)

E. Emmrich
Convergence of a time discretization for a class of non-Newtonian fluid flow
Commun. Math. Sci. 6 (2008) 4, pp. 827-843
(link to journal) (preliminary version as PDF) (PDF, 232,2 KB)

E. Emmrich
Error of the two-step BDF for the incompressible Navier-Stokes problem
M2AN Math. Model. Numer. Anal. 38 (2004) 5, pp. 757-764
(link to journal) (extended preprint version as PDF) (PDF, 229,2 KB)

E. Emmrich
Stability and convergence of the two-step BDF for the incompressible Navier-Stokes problem
Int. J. Nonlinear Sci. Numer. Simul. 5 (2004) 3, pp. 199-209
(link to journal) (preliminary version as PDF) (PDF, 565,6 KB)

E. Emmrich
Error analysis for the second order BDF discretization of the incompressible Navier-Stokes problem
In: M. Feistauer, R. Rannacher, K. Kozel (eds.), Numerical Modelling in Continuum Mechanics (Proc. of the 4th Summer Conference Prague, August 2000), pp. 98 - 106, Matfyzpress Prag 2001
(preliminary version as PDF) (PDF, 178,8 KB)

E. Emmrich
Error of the two-step BDF for the incompressible Navier-Stokes problem
Preprint No. 741, Institut für Mathematik, TU Berlin, August 2002.
(PDF) (PDF, 229,2 KB)

E. Emmrich
Hydrodynamische Stabilität beim instationären Navier-Stokes-Problem
In: Preprint MBI-94-3, Universität Magdeburg, April 1994

Diskretisierungsverfahren für stationäre Probleme

E. Emmrich
External approximation of nonlinear operator equations
Numer. Funct. Anal. Optim. 30 (2009) 5-6, pp. 486-498
(link to journal) (preliminary version as PDF) (PDF, 171,9 KB)

E. Emmrich
Supraconvergence and supercloseness of a discretisation for elliptic third-kind boundary-value problems on polygonal domains
Comput. Methods Appl. Math. 7 (2007) 2, pp. 135-162
(link to journal) (PDF) (PDF, 327,6 KB)

E. Emmrich and R. D. Grigorieff
Supraconvergence of a finite difference scheme for elliptic third kind boundary value problems in fractional order Sobolev spaces
Comput. Methods Appl. Math. 6 (2006) 2, pp. 154-177
(link to journal) (PDF) (PDF, 336,2 KB)

E. Emmrich
Supraconvergence of a non-uniform discretisation for an elliptic third-kind boundary-value problem with mixed derivatives
In: I. Farago, P. Vabishchevich, L. Vulkov (eds.), Finite Difference Methods: Theory and Applications. Proc. Fourth Intern. Conf. FDM: T&A (Lozenetz, Bulgaria, August 2006), Rousse 2007
(preliminary version as PDF) (PDF, 328,8 KB)

Sonstiges

M. Eisenmann and R. Kruse
Two quadrature rules for stochastic Itō-integrals with fractional Sobolev regularity (2017)
(arXiv version)

A. Eikmeier, E. Emmrich, and E. Schöll
Why more physics can help achieving better mathematics
Int. J. Dyn. Control 6 (2018) 3, pp. 973–981
(link to journal) (PDF)

E. Emmrich
A short note on piecewise constant and piecewise linear interpolation (2015)
(PDF)

E. Emmrich, R. W. Hoppe, and R. Kornhuber
Rolf Dieter Griegorieff. Applications of Functional Analysis
Comp. Methods Appl. Math. 13 (2013) 4, 411-413
(link to journal) (PDF)

H.-C. Kreusler and H. Yserentant
The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces
Numer. Math. 121 (2012) 4, pp. 781-802
(link to journal) (preliminary version as PDF) (PDF, 173,5 KB)

J. Behrndt and H.-C. Kreusler
Boundary relations and generalized resolvents of symmetric operators in Krein spaces
Integr. Eq. Oper. Theory 59 (2007), pp. 309 - 327
(link to journal) (preliminary version as PDF) (PDF, 198,2 KB)

E. Emmrich and H. Schmitt
Numerical treatment of a class of optimal control problems arising in economics
Optim. Meth. Software 21 (2006) 5, pp. 746-766
(link to journal) (preliminary version as PDF) (PDF, 239,5 KB)

E. Emmrich and J. Kaldasch
Mathematical analysis of the primary network effect. March 2007, 14 p.
(PDF) (PDF, 371,4 KB)

E. Emmrich
Wirtschaftsmathematik. Skript zur gleichnamigen Lehrveranstaltung an der International Business School (IBS) Berlin, Mai 2004.
(PDF) (PDF, 319,5 KB)

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