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The IMA Hot Topics workshop on compatible spatialdiscretizations
was held in 2004. This volume contains original contributions based
on the material presented there. A unique feature is the inclusion
of work that is representative of the recent developments in
compatible discretizations across a wide spectrum of disciplines in
computational science. Abstracts and presentation slides from the
workshop can be accessed on the internet.
The IMA Hot Topics workshop on compatible spatialdiscretizations
was held in 2004. This volume contains original contributions based
on the material presented there. A unique feature is the inclusion
of work that is representative of the recent developments in
compatible discretizations across a wide spectrum of disciplines in
computational science. Abstracts and presentation slides from the
workshop can be accessed on the internet.
Computational methods to approximate the solution of differential
equations play a crucial role in science, engineering, mathematics,
and technology. The key processes that govern the physical
world—wave propagation, thermodynamics, fluid flow, solid
deformation, electricity and magnetism, quantum mechanics, general
relativity, and many more—are described by differential
equations. We depend on numerical methods for the ability to
simulate, explore, predict, and control systems involving these
processes. The finite element exterior calculus, or FEEC, is a
powerful new theoretical approach to the design and understanding
of numerical methods to solve partial differential equations
(PDEs). The methods derived with FEEC preserve crucial geometric
and topological structures underlying the equations and are among
the most successful examples of structure-preserving methods in
numerical PDEs. This volume aims to help numerical analysts master
the fundamentals of FEEC, including the geometrical and functional
analysis preliminaries, quickly and in one place. It is also
accessible to mathematicians and students of mathematics from areas
other than numerical analysis who are interested in understanding
how techniques from geometry and topology play a role in numerical
PDEs.
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