A spectral mimetic least-squares method
We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1484076
- Alternate ID(s):
- OSTI ID: 1140934
- Report Number(s):
- SAND-2014-1827J; S0898122114004623; PII: S0898122114004623
- Journal Information:
- Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 68 Journal Issue: 11; ISSN 0898-1221
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
Web of Science
Similar Records
Mimetic difference approximations of partial differential equations
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements