QA225 : Finite Element Exterior Calculus For Evolution Problems
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2014
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Abstarct: Recent research has shown that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools
of Hilbert complexes. This led to the development of the Finite Element Exterior Calculus (FEEC) for a large class of linear elliptic problems. In this thesis, we develop another
distinct extension to the FEEC, namely to parabolic and hyperbolic evolution systems,
allowing for the treatment of geometric and other evolution problems. Our approach is
to combine the recent work on the FEEC for elliptic problems with a classical approach
to solving evolution problems via semi-discrete finite element methods, by viewing solutions to the evolution problem as lying in time-parameterized Hilbert spaces (or Bochner spaces).
Keywords:
#FEEC #Elliptic Equations #Evolution Equations #Apriori estimates Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: