Adaptive Linearly Implicit Methods for Linear Poroelastic Equations

Please always quote using this URN: urn:nbn:de:0297-zib-9312
  • Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Bodo Erdmann, Jens Lang, Sebastian Matera, Krzysztof Wilmanski
Document Type:ZIB-Report
Tag:Biot's model; Poroelasticity; Rosenbrock methods; adaptive finite elements; adaptive time integration; bone healing
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M50 Mesh generation and refinement
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
CCS-Classification:G. Mathematics of Computing / G.4 MATHEMATICAL SOFTWARE
Date of first Publication:2006/07/03
Series (Serial Number):ZIB-Report (06-37)