Publications

Scientific Articles in Journals and Books

Submitted
•	Philip Trautmann, Boris Vexler, Alexander Zlotnik: Finite element error analysis for measure-valued optimal control problems governed by the 1D generalized wave equation submitted, Preprint arXiv: 1702.00362, 2017.
•	Harald Garcke, Michael Hinze, Christian Kahle, Kei Fong Lam : A phase field approach to shape optimization in Navier-Stokes flow with integral state constraint submitted, Preprint arXiv: 1702.03855, 2017.
•	Harbir Antil, Johannes Pfefferer, Sergejs Rogovs: Fractional Operators with Inhomogeneous Boundary Conditions: Analysis, Control, and Discretization submitted, Preprint arXiv: 1703.05256, 2017.
•	Thomas Apel, Johannes Pfefferer, Max Winkler: Error estimates for the postprocessing approach applied to Neumann boundary control problems in polyhedral domains submitted, 2017.
•	Lucas Bonifacius, Ira Neitzel: Second Order Optimality Conditions for Optimal Control of Quasilinear Parabolic Equations submitted, 2017.
•	Thomas Apel, Mariano Mateos, Johannes Pfefferer, Arnd Rösch: Error estimates for Dirichlet control problems in polygonal domains submitted, Preprint arXiv: 1704.08843, 2017.
•	Dominik Meidner, Johannes Pfefferer, Klemens Schürholz, Boris Vexler: hp-Finite Elements for Fractional Diffusion submitted, Preprint arXiv: 1706.04066, 2017.
•	Malte Braack, Martin Quaas, Benjamin Tews, Boris Vexler: Optimization of fishing strategies in space and time as a non-convex optimal control problem submitted, 2017.
•	Dominik Meidner, Boris Vexler: Optimal Error Estimates for Fully Discrete Galerkin Approximations of Semilinear Parabolic Equations submitted, Preprint arXiv: 1707.07889, 2017.
•	Dmitriy Leykekhman, Boris Vexler: Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problems submitted, Preprint arXiv: 1707.09163, 2017.
•	Christian Kahle, Kei Fong Lam: Parameter identification via optimal control for a Cahn--Hilliard-chemotaxis system with a variable mobility submitted, Preprint arXiv: 1707.06853, 2017.
•	Michael Hintermüller, Michael Hinze, Christian Kahle, Tobias Keil: A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn-Hilliard-Navier-Stokes system submitted, 2016.
•	Harbir Antil, Johannes Pfefferer, Mahamadi Warma: A note on semilinear fractional elliptic equation: analysis and discretization submitted, Preprint arXiv: 1607.07704, 2016.
•	Harald Garcke, Michael Hinze, Christian Kahle: Optimal Control of time-discrete two-phase flow driven by a diffuse-interface model submitted, 2016.
•	Lucas Bonifacius, Konstantin Pieper: Strong Stability of Linear Parabolic Time-Optimal Control Problems submitted, 2016.
•	Anne-Celine Boulanger, Philip Trautmann: Sparse optimal control of the Korteweg-de Vries-Burgers equation on a bounded domain submitted, 2015.
•	Thomas Apel, Serge Nicaise, Johannes Pfefferer: A dual singular complement method for the numerical solution of the Poisson equation with L2 boundary data in non-convex domains submitted, Preprint arXiv: 1505.00414, 2015.

Appeared 2016
•	Karl Kunisch, Philip Trautmann, Boris Vexler: Optimal control of the undamped linear wave equation with measure valued controls SIAM Journal on Control and Optimization 54(3), pp. 1212-1244, 2016. (doi:10.1137/141001366)
•	Dmitriy Leykekhman, Boris Vexler: Finite element pointwise results on convex polyhedral domains SIAM Journal on Numerical Analysis 54(2), pp. 561–587, 2016. (doi:10.1137/15M1013912)
•	Dmitriy Leykekhman, Boris Vexler: A priori error estimates for three dimensional parabolic optimal control problems with pointwise control SIAM Journal on Control and Optimization, 54(5), pp. 2403-2435, 2016. (doi:10.1137/15M1028042)
•	Lukas Failer, Dominik Meidner, Boris Vexler: Optimal Control of a Linear Unsteady Fluid-Structure Interaction Problem Journal of Optimization Theory and Applications, 170(1), pp. 1-27, 2016. (doi:10.1007/s10957-016-0930-1)
•	Dmitriy Leykekhman, Boris Vexler: Pointwise best approximation results for Galerkin finite element solutions of parabolic problems SIAM Journal on Numerical Analysis 54(3), pp. 1365-1384, 2016. (doi:10.1137/15M103412X)
•	Thomas Apel, Serge Nicaise, Johannes Pfefferer: Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains Numer Methods Partial Differential Equations 32(5), pp. 1433-1454, 2016. (doi:10.1002/num.22057)
•	Harald Garcke, Michael Hinze, Christian Kahle: A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow Applied Numerical Mathematics 99, pp. 151-171, 2016. (doi:10.1016/j.apnum.2015.09.002)
•	Harald Garcke, Claudia Hecht, Michael Hinze, Christian Kahle, Kei Fong Lam: Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach Interfaces and Free Boundaries 18(2), pp. 219-261, 2016.

Appeared 2015
•	Anne-Céline Boulanger, Philippe Moireau, Benoit Perthame, Jacques Saint-Marie: Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description Communications in Mathematical Sciences 13(3), pp. 587-622, 2015. (doi:10.4310/CMS.2015.v13.n3.a1)
•	Thomas Apel, Mariano Mateos, Johannes Pfefferer, Arnd Rösch: On the regularity of the solutions of Dirichlet optimal control problems in polygonal domains SIAM Journal on Control and Optimization 53(6), pp. 3620-3641, 2015. (doi:10.1137/140994186)
•	Bernhard Kiniger: A Transformation Approach in Shape Optimization: Existence and Regularity Results Numerical Functional Analysis and Optimization, 36(12), pp. 1585-1621, 2015. (doi:10.1080/01630563.2015.1076001)
•	Dominik Meidner, Thomas Richter: A Posteriori Error Estimation for the Fractional Step Theta Discretization of the Incompressible Navier-Stokes Equations Computer Methods in Applied Mechanics and Engineering 288, pp. 45-59, 2015. (doi:10.1016/j.cma.2014.11.031)
•	Ira Neitzel, Johannes Pfefferer, Arnd Rösch: Finite element discretization of state-constrained elliptic optimal control problems with semilinear state equation SIAM Journal on Control and Optimization, 53(2), pp. 874-904, 2015. (doi:10.1137/140960645)
•	Eduardo Casas, Boris Vexler, Enrique Zuazua: Sparse initial data identification for parabolic PDE and it´s finite element approximations Mathematical Control and Related Fields 5(3), pp. 377-399, 2015. (doi:10.3934/mcrf.2015.5.377)
•	Karl Kunisch, Konstantin Pieper, Armin Rund: Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - a monolithic approach ESAIM: Mathematical Modelling and Numerical Analysis, published online, 2015. (doi:10.1051/m2an/2015048)
•	Mariano Mateos, Ira Neitzel: Dirichlet control of elliptic state constrained problems Computational Optimization and Applications, published online, 2015. (doi:10.1007/s10589-015-9784-y)
•	Thomas Apel, Johannes Pfefferer, Max Winkler: Local Mesh Refinement for the Discretisation of Neumann Boundary Control Problems on Polyhedra Mathematical Methods in the Applied Sciences, published online, 2015. (doi:10.1002/mma.3566)
•	Klaus Krumbiegel, Johannes Pfefferer: Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations Computational Optimization and Applications 61(2), pp. 373-408, 2015. (doi:10.1007/s10589-014-9718-0)
•	Thomas Apel, Johannes Pfefferer, Arnd Rösch: Finite element error estimates on the boundary with application to optimal control Mathematics of Computation 84, pp. 33-70, 2015. (doi:10.1090/S0025-5718-2014-02862-7)
•	Harald Garcke, Claudia Hecht, Michael Hinze, Christian Kahle: Numerical approximation of phase field based shape and topology optimization for fluids SIAM Journal on Scientific Computing, 2015. (doi:10.1137/140969269)

Appeared 2014
•	Dominik Meidner, Thomas Richter: Goal-Oriented Error Estimation for the Fractional Step Theta Scheme Computational Methods in Applied Mathematics 14(2), pp. 203-220, 2014. (doi:10.1515/cmam-2014-0002)
•	Andreas Springer, Boris Vexler: Third Order Convergent Time Discretization for Parabolic Optimal Control Problems with Control Constraints Computational Optimization and Applications 57(1), pp. 205-240, 2014. (doi:10.1007/s10589-013-9580-5)
•	Pedro Merino, Ira Neitzel, Fredi Tröltzsch: An Adaptive Numerical Method for Semi-Infinite Elliptic Control Problems Based on Error Estimates Optimization Methods and Software, 30(3), pp. 492-515, 2014. (doi:10.1080/10556788.2014.932789)
•	Eduardo Casas, Mariano Mateos, Boris Vexler: New Regularity Results and Improved Error Estimates for Optimal Control Problems with State Constraints ESAIM: Control, Optimisation and Calculus of Variations 20(3), pp. 803-822, 2014. (doi:10.1051/cocv/2013084)
•	Barbara Kaltenbacher, Alana Kirchner, Boris Vexler: Goal oriented adaptivity in the IRGNM for parameter identification in PDEs II: All-at-once formulations Inverse Problems, 30(4), 045002, 2014. (doi:10.1088/0266-5611/30/4/045002)
•	Barbara Kaltenbacher, Alana Kirchner, Slobodan Veljovic: Goal oriented adaptivity in the IRGNM for parameter identification in PDEs I: Reduced formulation Inverse Problems, 30(4), 045001, 2014. (doi:10.1088/0266-5611/30/4/045001)
•	Bernhard Kiniger, Jinming Lu, Gerwin Riedl, Ewald A. Werner: Three-dimensional tool design for steady-state electrochemical machining by continuous adjoint-based shape optimization Chemical Engineering Science 106, pp. 198-210, 2014. (doi:10.1016/j.ces.2013.11.040)
•	Karl Kunisch, Konstantin Pieper, Boris Vexler: Measure valued directional sparsity for parabolic optimal control problems SIAM Journal on Control and Optimization 52(5), pp. 3078-3108, 2014. (doi:10.1137/140959055)

Appeared 2013
•	Dmitriy Leykekhman, Dominik Meidner, Boris Vexler: Optimal Error Estimates for Finite Element Discretization of Elliptic Optimal Control Problems with Finitely Many Pointwise State Constraints Computational Optimization and Applications 55(3), pp. 769-802, 2013. (doi:10.1007/s10589-013-9537-8)
•	Konstantin Pieper, Boris Vexler: A Priori Error Analysis for Discretization of Sparse Elliptic Optimal Control Problems in Measure Space SIAM Journal on Control and Optimization 51(4), pp. 2788-2808, 2013. (doi:10.1137/120889137)
•	Dmitriy Leykekhman, Boris Vexler: Optimal a Priori Error Estimates of Parabolic Optimal Control Problems with Pointwise Control SIAM Journal on Numerical Analysis 51(5), pp. 2797-2821, 2013. (doi:10.1137/120885772)
•	Sandra May, Rolf Rannacher, Boris Vexler: Error Analysis for a Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems SIAM Journal on Control and Optimization 51 (3), pp. 2585-2611, 2013. (doi:10.1137/080735734)
•	Bernhard Kiniger, Boris Vexler: A Priori Error Estimates for Finite Element Discretizations of a Shape Optimization Problem ESAIM: Mathematical Modelling and Numerical Analysis 47(6), pp. 1733-1763, 2013. (doi:10.1051/m2an/2013086)
•	Thomas Richter, Andreas Springer, Boris Vexler: Efficient Numerical Realization of Discontinuous Galerkin Methods for Temporal Discretization of Parabolic Problems Numerische Mathematik 124(1), pp. 151-182, 2013. (doi:10.1007/s00211-012-0511-7)
•	Anne-Céline Boulanger, Marie-Odile Bristeau, Jacques Saint-Marie: Analytical solutions for the free surface hydrostatic Euler equations Communications in Mathematical Sciences 11(4), pp. 993-1010, 2013. (doi:10.4310/CMS.2013.v11.n4.a5)
•	Olivier Bernard, Anne-Céline Boulanger, Marie-Odile Bristeau, Jacques Saint-Marie: A 2D model for hydrodynamics and biology coupling applied to algae growth simulations ESAIM: Mathematical Modelling and Numerical Analysis 47(5), pp. 1387-1412, 2013. (doi:10.1051/m2an/2013072)
•	Michael Hintermüller, Michael Hinze,Christian Kahle: An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system Journal of Computational Physics 235, pp. 810-827, 2013. (doi:10.1016/j.jcp.2012.10.010)

Appeared 2012
•	Ira Neitzel, Boris Vexler: A Priori Error Estimates for Space-Time Finite Element Discretization of Semilinear Parabolic Optimal Control Problems Numerische Mathematik 120(2), pp. 345-386, 2012. (doi:10.1007/s00211-011-0409-9)
•	Klaus Krumbiegel, Ira Neitzel, Arnd Rösch: Regularization for Semilinear Elliptic Optimal Control Problems with Pointwise State and Control Constraints Computational Optimization and Applications 52(1), pp. 181-207, 2012. (doi:10.1007/s10589-010-9357-z)
•	Thomas Apel, Johannes Pfefferer, Arnd Rösch: Finite Element Error Estimates for Neumann Boundary Control Problems on Graded Meshes Computational Optimization and Applications 52(1), pp. 3-28, 2012. (doi:10.1007/s10589-011-9427-x)

Appeared 2011
•	Alana Kirchner, Dominik Meidner, Boris Vexler: Trust Region Methods with Hierarchical Finite Element Models for PDE-Constrained Optimization Control and Cybernetics 40(4), pp. 1019-1042, 2011.
•	Dominik Meidner, Boris Vexler: A Priori Error Analysis of the Petrov-Galerkin Crank-Nicolson Scheme for Parabolic Optimal Control Problems SIAM Journal on Control and Optimization 49(5), pp. 2183-2211, 2011. (doi:10.1137/100809611)
•	Dominik Meidner, Rolf Rannacher, Boris Vexler: A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time SIAM Journal on Control and Optimization 49(5), pp. 1961-1997, 2011. (doi:10.1137/100793888)
•	Barbara Kaltenbacher, Alana Kirchner, Boris Vexler: Adaptive Discretizations for the Choice of a Tikhonov Regularization Parameter in Nonlinear Inverse Problems Inverse Problems 27(12), 2011. (doi:10.1088/0266-5611/27/12/125008)
•	Axel Kröner, Karl Kunisch, Boris Vexler: Semismooth Newton Methods for Optimal Control of the Wave Equation with Control Constraints SIAM Journal on Control and Optimization 49(2), pp. 830-858, 2011. (doi:10.1137/090766541)
•	Thomas Apel, Olaf Benedix, Dieter Sirch, Boris Vexler: A Priori Mesh Grading for an Elliptic Problem with Dirac Right-hand Side SIAM Journal on Numerical Analysis 49(3), pp. 992-1005, 2011. (doi:10.1137/090778018)
•	Ira Neitzel, Uwe Prüfert, Thomas Slawig: A Smooth Regularization of the Projection Formula for Constrained Parabolic Optimal Control Problems Numerical Functional Analysis and Optimization 32(12), pp. 1283-1315, 2011. (doi:10.1080/01630563.2011.597915)
•	Pedro Merino, Ira Neitzel, Fredi Tröltzsch: On Linear-Quadratic Elliptic Control Problems of Semi-Infinite Type Applicable Analysis 90(6), pp. 1047-1074, 2011. (doi:10.1080/00036811.2010.489187)

Appeared 2010
•	Pedro Merino, Fredi Tröltzsch, Boris Vexler: Error Estimates for the Finite Element Approximation of a Semilinear Elliptic Control Problem with State Constraints and Finite Dimensional Control Space ESAIM: Mathematical Modelling and Numerical Analysis 44(1), pp. 167-188, 2010. (doi:10.1051/m2an/2009045)
•	Klaus Krumbiegel, Ira Neitzel, Arnd Rösch: Sufficient Optimality Conditions for the Moreau-Yosida-Type Regularization Concept Applied to Semilinear Elliptic Optimal Control Problems with Pointwise State Constraints Mathematics and its Applications - Annals of AOSR 2(2), pp. 222-246, 2010.
•	Pedro Merino, Ira Neitzel, Fredi Tröltzsch: Error Estimates for the Finite Element Discretization of Semi-infinite Elliptic Optimal Control Problems Discussiones Mathematicae. Differential Inclusions, Control and Optimization 30(2), pp. 221-236, 2010.

Appeared 2009
•	Dominik Meidner, Rolf Rannacher, Jevgeni Vihharev: Goal-Oriented Error Control of the Iterative Solution of Finite Element Equations Journal of Numerical Mathematics 17(2), pp. 143-172, 2009. (doi:10.1515/JNUM.2009.009)
•	Olaf Benedix, Boris Vexler: A Posteriori Error Estimation and Adaptivity for Elliptic Optimal Control Problems with State Constraints Computational Optimization and Applications 44(1), pp. 3-25, 2009. (doi:10.1007/s10589-008-9200-y)
•	Axel Kröner, Boris Vexler: A Priori Error Estimates for Elliptic Optimal Control Problems with Bilinear State Equation Journal of Computational and Applied Mathematics 230(2), pp. 781-802, 2009. (doi:10.1016/j.cam.2009.01.023)
•	Ira Neitzel, Fredi Tröltzsch: On Regularization Methods for the Numerical Solution of Parabolic Control Problems with Pointwise State Constraints ESAIM: Control, Optimisation and Calculus of Variations 15 (2), pp. 426-453, 2009. (doi:10.1051/cocv:2008038)
•	Ira Neitzel, Uwe Prüfert, Thomas Slawig: Strategies for Time-Dependent PDE Control with Inequality Constraints Using an Integrated Modeling and Simulation Environment Numerical Algorithms 50, pp. 241-269, 2009. (doi:10.1007/s11075-008-9225-4)

Appeared 2008
•	Dominik Meidner, Boris Vexler: A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems. Part II: Problems with Control Constraints SIAM Journal on Control and Optimization 47(3), pp. 1301-1329, 2008. (doi:10.1137/070694028)
•	Dominik Meidner, Boris Vexler: A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems. Part I: Problems without Control Constraints SIAM Journal on Control and Optimization 47(3), pp. 1150-1177, 2008. (doi:10.1137/070694016)
•	Samuel Amstutz, Takeo Takahashi, Boris Vexler: Topological Sensitivity Analysis for Time-Dependent Problems ESAIM: Control, Optimisation and Calculus of Variations 14(3), pp. 427-455, 2008. (doi:10.1051/cocv:2007059)
•	Michael Schmich, Boris Vexler: Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations SIAM Journal on Scientific Computing 30(1), pp. 369-393, 2008. (doi:10.1137/060670468)
•	Boris Vexler, Winnifried Wollner: Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints SIAM Journal on Control and Optimization 47(1), pp. 509-534, 2008. (doi:10.1137/070683416)
•	Anke Griesbaum, Barbara Kaltenbacher, Boris Vexler: Efficient Computation of the Tikhonov Regularization Parameter by Goal Oriented Adaptive Discretization Inverse Problems 24(2), 2008. (doi:10.1088/0266-5611/24/2/025025)
•	Juan Carlos de los Reyes, Christian Meyer, Boris Vexler: Finite Element Error Analysis for State-Constrained Optimal Control of the Stokes Equations Control and Cybernetics 37(2), pp. 251-284, 2008.
•	Ira Neitzel, Fredi Tröltzsch: On Convergence of Regularization Methods for Nonlinear Parabolic Optimal Control Problems with Control and State Constraints Control and Cybernetics 37(4), pp. 1013-1043, 2008.

Appeared 2007
•	Dominik Meidner, Boris Vexler: Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems SIAM Journal on Control and Optimization 46(1), pp. 116-142, 2007. (doi:10.1137/060648994)
•	Roland Becker, Dominik Meidner, Boris Vexler: Efficient Numerical Solution of Parabolic Optimization Problems by Finite Element Methods Optimization Methods and Software 22(5), pp. 813-833, 2007. (doi:10.1080/10556780701228532)
•	Boris Vexler: Finite Element Approximation of Elliptic Dirichlet Optimal Control Problems Numerical Functional Analysis and Optimization 28(7-8), pp. 957-973, 2007. (doi:10.1080/01630560701493305)
•	Roland Griesse, Boris Vexler: Numerical Sensitivity Analysis for the Quantity of Interest in PDE-constrained Optimization SIAM Journal on Scientific Computing 29(1), pp. 22-48, 2007. (doi:10.1137/050637273)
•	Roland Becker, Boris Vexler: Optimal Control of the Convection-Diffusion Equation Using Stabilized Finite Element Methods Numerische Mathematik 106(3), pp. 349-367, 2007. (doi:10.1007/s00211-007-0067-0)
•	Karl Kunisch, Boris Vexler: Optimal Vortex Reduction for Instationary Flows based on Translation Invariant Cost Functionals SIAM Journal on Control and Optimization 46(4), pp. 1368-1397, 2007. (doi:10.1137/050632774)
•	Karl Kunisch, Boris Vexler: Constrained Dirichlet Boundary Control in L² for a Class of Evolution Equations SIAM Journal on Control and Optimization 46(5), 1726-1753, 2007. (doi:10.1137/060670110)

Appeared 2006
•	Arnd Rösch, Boris Vexler: Optimal Control of the Stokes Equations: A Priori Error Analysis for Finite Element Discretization with Postprocessing SIAM Journal on Numerical Analysis 44(5), 1903-1920, 2006. (doi:10.1137/050637364)

Appeared 2005
•	Roland Becker, Boris Vexler: Mesh Refinement and Numerical Sensitivity Analysis for Parameter Calibration of Partial Differential Equations Journal of Computational Physics 206(1), pp. 95-110, 2005. (doi:10.1016/j.jcp.2004.12.018)
•	Roland Becker, Malte Braack, Boris Vexler: Parameter Identification for Chemical Models in Combustion Problems Applied Numerical Mathematics 54(3-4), pp. 519-536, 2005. (doi:10.1016/j.apnum.2004.09.017)
•	Rolf Rannacher, Boris Vexler: A Priori Error Estimates for the Finite Element Discretization of Elliptic Parameter Identification Problems with Pointwise Measurements SIAM Journal on Control and Optimization 44(5), pp. 1844-1863, 2005. (doi:10.1137/040611100)

Appeared 2004
•	Roland Becker, Boris Vexler: A Posteriori Error Estimation for Finite Element Discretization of Parameter Identification Problems Numerische Mathematik 96(3), pp. 435-459, 2004. (doi:10.1007/s00211-003-0482-9)
•	Roland Becker, Malte Braack, Boris Vexler: Numerical Parameter Estimation for Chemical Models in Multidimensional Reactive Flows Combustion Theory and Modelling 8(4), pp. 661-682, 2004. (doi:10.1088/1364-7830/8/4/001)