Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems

Please always quote using this URN: urn:nbn:de:0297-zib-5892
  • 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.

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Author:Jens Lang, Bodo Erdmann
Document Type:ZIB-Report
Tag:Nonlinear time-dependent PDEs; Rosenbrock methods; a posteriori error estimates; local refinement; multilevel finite elements
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:2000/06/20
Series (Serial Number):ZIB-Report (00-21)
Published in:Appeared in: A. V. Wouver; P. Saucez; W. E. Schiesser (eds.), Adaptive Method of Lines, Chapman and Hall, CRC, 2001, ISBN: 1-58488-231-X, pp. 295-316