This paper introduces and analyses a local, residual-based a posteriori error indicator for the Morley finite element method of the biharmonic Kirchhoff plate bending problem. In the theoretical part of the paper, a recent approach presented by the authors for clamped boundaries is extended to general boundary conditions. The error indicator is proven to be both reliable and efficient. The numerical part of the paper presents a set of results on various benchmark computations with different kinds of domains and boundary conditions. These tests verify the reliability and efficiency of the error estimator and illustrate the robustness of the method for adaptive mesh refinements. Copyright © 2009 John Wiley & Sons, Ltd.
domingo, 3 de enero de 2010
A posteriori error analysis for the Morley plate element with general boundary conditions
This paper introduces and analyses a local, residual-based a posteriori error indicator for the Morley finite element method of the biharmonic Kirchhoff plate bending problem. In the theoretical part of the paper, a recent approach presented by the authors for clamped boundaries is extended to general boundary conditions. The error indicator is proven to be both reliable and efficient. The numerical part of the paper presents a set of results on various benchmark computations with different kinds of domains and boundary conditions. These tests verify the reliability and efficiency of the error estimator and illustrate the robustness of the method for adaptive mesh refinements. Copyright © 2009 John Wiley & Sons, Ltd.
Optimal Management of a Bioreactor for Eutrophicated Water Treatment: A Numerical Approach
Abstract This paper presents a numerical algorithm for computing the optimal design variables in the management of a bioreactor for
the treatment of eutrophicated water: initial and distributed quantities of phytoplankton added along the process, and total
duration of the process. This real-world problem is formulated as a state-control constrained optimal control problem, whose
numerical resolution is the main aim of this study. After discretizing the control problem, we present a structured algorithm
for solving the discrete state systems, computing the corresponding derivatives, and minimizing the objective function. Finally,
the good performance of the algorithm is shown by applying it to a realistic example with two pre-reservoirs.
the treatment of eutrophicated water: initial and distributed quantities of phytoplankton added along the process, and total
duration of the process. This real-world problem is formulated as a state-control constrained optimal control problem, whose
numerical resolution is the main aim of this study. After discretizing the control problem, we present a structured algorithm
for solving the discrete state systems, computing the corresponding derivatives, and minimizing the objective function. Finally,
the good performance of the algorithm is shown by applying it to a realistic example with two pre-reservoirs.
- Content Type Journal Article
- DOI 10.1007/s10915-009-9344-7
- Authors
- Lino J. Alvarez-Vázquez, Universidad de Vigo Departamento Matemática Aplicada II, ETSI Telecomunicación 36310 Vigo Spain
- Francisco J. Fernández, Universidad de Santiago de Compostela Departamento Matemática Aplicada, Facultad de Matemáticas 15782 Santiago Spain
- Aurea Martínez, Universidad de Vigo Departamento Matemática Aplicada II, ETSI Telecomunicación 36310 Vigo Spain
- Journal Journal of Scientific Computing
- Online ISSN 1573-7691
- Print ISSN 0885-7474
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