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BEM-based Finite Element Approaches on Polytopal Meshes (Hardcover, 1st ed. 2019)
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BEM-based Finite Element Approaches on Polytopal Meshes (Hardcover, 1st ed. 2019)
Series: Lecture Notes in Computational Science and Engineering, 130
Expected to ship within 12 - 19 working days
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This book introduces readers to one of the first methods developed
for the numerical treatment of boundary value problems on polygonal
and polyhedral meshes, which it subsequently analyzes and applies
in various scenarios. The BEM-based finite element approaches
employs implicitly defined trial functions, which are treated
locally by means of boundary integral equations. A detailed
construction of high-order approximation spaces is discussed and
applied to uniform, adaptive and anisotropic polytopal meshes. The
main benefits of these general discretizations are the flexible
handling they offer for meshes, and their natural incorporation of
hanging nodes. This can especially be seen in adaptive finite
element strategies and when anisotropic meshes are used. Moreover,
this approach allows for problem-adapted approximation spaces as
presented for convection-dominated diffusion equations. All
theoretical results and considerations discussed in the book are
verified and illustrated by several numerical examples and
experiments. Given its scope, the book will be of interest to
mathematicians in the field of boundary value problems, engineers
with a (mathematical) background in finite element methods, and
advanced graduate students.
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