Combining Time and Mimetic Spatial Discretizations

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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Steinberg, Stanly

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Title

Combining Time and Mimetic Spatial Discretizations

Title of Series

Connections in Geometric Numerical Integration and Structure-Preserving Discretization (17w5152)

Number of Parts

Author

Steinberg, Stanly

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.14288/1.0361786 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Release Date

2017

Language

English

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Subject Area

Computer Science Mathematics

Genre

Workshop/Interactive Format Lecture

Abstract

The problem is to combine explicit time and mimetic spatial discretizations for wave equations so that the energy is conserved. It is easy to see that intuitive discretizations of the energy are not conserved. However it is possible to find conserved quantities that depend on the time step that are conserved and converge quadratically in the time step to the classical energy.