Mathematics – Spectral Theory
Scientific paper
Jun 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979pepi...19..158t&link_type=abstract
(Lunar and Planetary Institute and NASA, Workshop on Solid Convection in the Terrestrial Planets, Moffett Field, Calif., Dec. 12
Mathematics
Spectral Theory
Finite Difference Theory, Finite Element Method, Free Convection, Solid State, Terrestrial Planets, Three Dimensional Flow, Adiabatic Flow, Boussinesq Approximation, Rheology, Spectral Theory, Stress-Strain Relationships, Time Dependence, Two Dimensional Flow, Planets, Terrestrial Planets, Convection, Mathematical Models, Review, Interiors, Comparisons, Techniques, Rheology, Boundary Layers, Flow, Time Dependency, Thermal Effects, Pressure, Temperatures, Density, Parameters, Viscosity, Modal Analysis
Scientific paper
The finite element, finite difference and spectral methods for the calculation of finite-amplitude thermal convection in planetary interiors are examined. The applications of each class of approach are outlined and the methods are compared for the case of three dimensional solid-state convection with a realistic rheology. Although finite difference methods have met with some success to date, it is concluded that future developments are likely to favor finite element methods when rheology and boundaries are complex, and spectral methods when accuracy is important and the rheology and boundaries are simple.
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