TY - CHAP A1 - Deuflhard, Peter A1 - Lang, Jens A1 - Nowak, Ulrich ED - Neunzert, H. T1 - Recent Progress in Dynamical Process Simulation T2 - Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94) Y1 - 1996 SP - 122 EP - 137 PB - Wiley & Teubner ER - TY - THES A1 - Lang, Jens T1 - Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems. Theory, Algorithm, and Applications N2 - This monograph has been written to illustrate the interlocking of theory, algorithm, and application in developing solution techniques for complex PDE systems. A deep theoretical understanding is necessary to produce a powerful idea leading to a successful algorithm. Efficient and robust implementation is the key to make the algorithm perform satisfactorily. The extra insight obtained by solving real--life problems brings out the structure of the method more clearly and suggests often ways to improve the numerical algorithm. It is my intention to impart the beauty and complexity found in both the theoretical investigation of the adaptive algorithm proposed here, i.e., the coupling of Rosenbrock methods in time and multilevel finite elements in space, and its realization. I hope that this method will find many more interesting applications. T3 - ZIB-Report - SC-99-20 KW - Adaptive multilevel finite elements KW - Rosenbrock methods KW - a posteriori error estimates KW - Rothe method Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4089 ER - TY - GEN A1 - Lang, Jens A1 - Erdmann, Bodo T1 - Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems N2 - Dynamical process simulation of complex real-life problems often requires the use of modern algorithms, which automatically adapt both the time and space discretization in order to get error-controlled approximations of the solution. In this paper, a combination of linearly implicit time integrators of Rosenbrock type and adaptive multilevel finite elements based on a posteriori error estimates is presented. This approach has proven to work quite satisfactorily for a wide range of challenging practical problems. We show the performance of our adaptive method for two applications that arise in the study of flame balls and brine transport in porous media. T3 - ZIB-Report - 00-21 KW - Nonlinear time-dependent PDEs KW - Rosenbrock methods KW - multilevel finite elements KW - local refinement KW - a posteriori error estimates Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5892 ER - TY - GEN A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian A1 - Deuflhard, Peter T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible N2 - By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. T3 - ZIB-Report - 01-14 KW - mandible KW - sensitivity analysis KW - finite element method KW - adaptive grid refinement Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6403 ER -