Adaptive Finite Elements in the Discretization of Parabolic Problems
By (author) Christian A Moller
Paperback (Published)
(March 2011)
ISBN: 9783832528157
5.75 x 8.31 inches
Price: $59.00
On back order
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.
- By (author) Christian A Moller
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Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory
Rigorous Existence and Convergence Results for the Boundary Value Problems
Volume 31
The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions
Volume 12
Effective Theories for Brittle Materials
A Derivation of Cleavage Laws and Linearized Griffith Energies from Atomistic and Continuum Nonlinear Models
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