@inproceedings{FroehlichDeuflhard1996, author = {Fr{\"o}hlich, Jochen and Deuflhard, Peter}, title = {An adaptive Galerkin method for the PDF transport equation of turbulent reactive flows}, booktitle = {Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)}, editor = {Neunzert, H.}, publisher = {Wiley \& Teubner}, pages = {176 -- 184}, year = {1996}, language = {en} } @misc{FroehlichLang1996, author = {Fr{\"o}hlich, Jochen and Lang, Jens}, title = {Twodimensional Cascadic Finite Element Computations of Combustion Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2167}, number = {SC-96-05}, year = {1996}, abstract = {We present an integrated time--space adaptive finite element method for solving systems of twodimensional nonlinear parabolic systems in complex geometry. The partial differential system is first discretized in time using a singly linearly implicit Runge--Kutta method of order three. Local time errors for the step size control are defined by an embedding strategy. These errors are used to propose a new time step by a PI controller algorithm. A multilevel finite element method with piecewise linear functions on unstructured triangular meshes is subsequently applied for the discretization in space. The local error estimate of the finite element solution steering the adaptive mesh refinement is obtained solving local problems with quadratic trial functions located essentially at the edges of the triangulation. This two--fold adaptivity successfully ensures an a priori prescribed tolerance of the solution. The devised method is applied to laminar gaseous combustion and to solid--solid alloying reactions. We demonstrate that for such demanding applications the employed error estimation and adaption strategies generate an efficient and versatile algorithm.}, language = {en} } @misc{FroehlichSchneider1996, author = {Fr{\"o}hlich, Jochen and Schneider, Kai}, title = {Computation of Decaying Turbulence in an Adaptive Wavelet Basis}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2227}, number = {SC-96-11}, year = {1996}, abstract = {The paper presents computations of decaying two--dimensional turbulence in an adaptive wavelet basis. At each time step the vorticity is represented by an adaptively selected set of wavelet functions which adjusts to the instantaneous distribution of vorticity. The results of this new algorithm are compared to a classical Fourier method and a Fourier method supplemented with wavelet compression in each time step.}, language = {en} } @misc{FroehlichLangRoitzsch1996, author = {Fr{\"o}hlich, Jochen and Lang, Jens and Roitzsch, Rainer}, title = {Selfadaptive Finite Element Computations with Smooth Time Controller and Anisotropic Refinement}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2270}, number = {SC-96-16}, year = {1996}, abstract = {We present Multilevel Finite Element computations for twodimensional reaction-diffusion systems modelling laminar flames. These systems are prototypes for extreme stiffness in time and space. The first of these two rather general features is accounted for by an improved control mechanism for the time step. The second one is reflected through very thin travelling reaction fronts for which we propose an anisotropic discretization by local directional refinement.}, language = {en} }