PUMA publications for /group/simtech/errorFri Jul 20 10:54:15 CEST 2018IMA J. Numer. Anal.4917--936Convergence rates for adaptive finite elements292009a estimator, equations posteriori adaptive error refinement, vorlaeufig elliptic mesh Fri Jul 20 10:54:15 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical ModellingA-posteriori error estimation for parameterized kernel-based systems2012subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, parameterized projection estimates, model vorlaeufig reduction, This work is concerned with derivation of fully offine/online decomposable effcient aposteriori error estimators for reduced parameterized nonlinear kernel-based systems. The dynamical systems under consideration consist of a nonlinear, time- and parameter-dependent kernel expansion representing the system's inner dynamics as well as time- and parameter-affne inputs, initial conditions and outputs. The estimators are established for a reduction technique originally proposed in [7] and are an extension of the estimators derived in [11] to the fully time-dependent, parameterized setting. Key features for the effcient error estimation are to use local Lipschitz constants provided by a certain class of kernels and an iterative scheme to balance computation cost against estimation sharpness. Together with the affnely time/parameter-dependent system components a full offine/online decomposition for both the reduction process and the error estimators is possible. Some experimental results for synthetic systems illustrate the effcient evaluation of the derived error estimators for different parameters.Fri Jul 20 10:54:15 CEST 2018Mathematical Models \& Methods in Applied Sciences111849--1881Design and Convergence of {AFEM} in ${H}({\rm div})$172007A convergence; posteriori reduction; error estimate; multigrid oscillation; preconditioning vorlaeufig We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A-?div in H(div, O). For A being a variable coefficient matrix with possible jump discontinuities, we provide a complete a posteriori error analysis which applies to both Raviart�Thomas RFri Jul 20 10:54:15 CEST 2018Advances in Computational Mathematics51131--1157Reduced basis approximation and a-posteriori error estimation for the coupled {S}tokes-{D}arcy system412015Error decomposition; medium 76D07 Porous Reduced method; basis problem; Stokes estimation; 76S05; equation; Non-coercive Domain flow; vorlaeufig 65N55; Fri Jul 20 10:54:15 CEST 2018SubmittedA convergent time-space adaptive $dG(s)$ finite element method for parabolic problems motivated by equal error distribution2017a equation estimators, convergence, error finite methods, posteriori adaptivity, element vorlaeufig heat Fri Jul 20 10:54:15 CEST 2018Numerical Methods for Partial Differential Equations41018--1042A posteriori error estimates with point sources in fractional sobolev spaces332017a Dirac estimators, error finite fractional methods, posteriori adaptivity, element spaces mass, Sobolev vorlaeufig Fri Jul 20 10:54:15 CEST 2018Systems and Control Letters1203 - 211Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems612012subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, projection estimates, model vorlaeufig reduction, In this paper, we consider the topic of model reduction for nonlinear dynamical systems based on kernel expansions. Our approach allows for a full offline/online decomposition and efficient online computation of the reduced model. In particular, we derive an a-posteriori state-space error estimator for the reduction error. A key ingredient is a local Lipschitz constant estimation that enables rigorous a-posteriori error estimation. The computation of the error estimator is realized by solving an auxiliary differential equation during online simulations. Estimation iterations can be performed that allow a balancing between estimation sharpness and computation time. Numerical experiments demonstrate the estimation improvement over different estimator versions and the rigor and effectiveness of the error bounds.