A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling
A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling (International Series of Numerical Mathematics) Jörg Steinbach,
Publisher: Birkhauser
ISBN: 376436582X
Edition: Hardcover; 2002-03-22
Summary:
This monograph is devoted to the study of an evolutionary variational
inequality approach to a degenerate moving free boundary problem. The
inequality approach of obstacle type results from the application of
an integral transformation. It takes an intermediate position between
elliptic and parabolic inequalities and comprises an elliptic
differential operator, a memory term and time-dependent convex
constraint sets. The study of such inequality problems is motivated
by applications to injection and compression moulding, to
electro-chemical machining and other quasi-stationary Stefan type
problems.The mathematical analysis of the problem covers existence,
uniqueness, regularity and time evolution of the solution. This is
carried out in the framework of the variational inequality theory.
The numerical solution in two and three space dimensions is discussed
using both finite element and finite volume approximations. Finally,
a description of injection and compression moulding is presented in
terms of different mathematical models, a generalized Hele-Shaw flow,
a distance concept and Navier-Stokes flow. This volume is primarily
addressed to applied mathematicians working in the field of nonlinear
partial differential equations and their applications, especially
those concerned with numerical aspects. However, the book will also
be useful for scientists from the application areas, in particular,
applied scientists from engineering and physics.
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