Adaptive Finite Elements in the Discretization of Parabolic Problems

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Logos Verlag Berlin GmbH, 2011 - Mathematics - 248 pages
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Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods for time dependent problems. In this context, aspects of temporal adaptivity and error control are considered in particular. Based on the gained insights, a specific adaptive algorithm is designed and analyzed thoroughly. Most importantly, it is proven that the presented adaptive method terminates within any demanded error tolerance. Moreover, the developed algorithm is analyzed from a numerical point of view and its performance is compared to well-known standard methods. Finally, it is applied to the real-life problem of concrete carbonation, where two different discretizations are compared.
 

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Contents

1
2
3
8
2
23
Discretization of parabolic PDEs
44
The adaptive algorithm ASTFEM
105
Numerical aspects of ASTFEM
169
13
184
Application to carbonation problem
199
36
226
47
245
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