Multiscale Finite Element Methods For Second Order Elliptic BVPs - Akhtar, Md Selim
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In this book the convergence of the multiscale finite element method (MsFEM) for second order elliptic equations with oscillating coefficient in two space dimension is studied. Such equations often arise in composite materials and flows in porous media. The main purpose is to understand the theoretical background of this method and its convergence analysis. The oscillating coefficient is assumed to be of two scales and is periodic in the large scale. The MsFEM is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the…mehr

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Produktbeschreibung
In this book the convergence of the multiscale finite element method (MsFEM) for second order elliptic equations with oscillating coefficient in two space dimension is studied. Such equations often arise in composite materials and flows in porous media. The main purpose is to understand the theoretical background of this method and its convergence analysis. The oscillating coefficient is assumed to be of two scales and is periodic in the large scale. The MsFEM is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution. This is accomplished by incorporating the local microstructure of the differential operator into the finite element base functions. As a consequence, the base functions are adapted to the local properties of the differential operator.
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Autorenporträt
Md Selim Akhtar is working as a Software Engineer at TCS Ltd. Prior to TCS; he worked at Laboratorio di Elettrotecnica ed Elettromagnetismo Computazionale, Dipartimento di Ingegneria Elettrica, Universita di Padova, Italy as a Research Associate. He completed M.Sc. from Indian Institute of Technology, Guwahati and B.Sc. from AMU, Aligarh.