Open AccessVariational principles for the momentum equation of mantle convection with Newtonian and power‐law rheologies
Author(s) -
Matyska Ctirad
Publication year - 1996
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1996.tb05286.x
Subject(s) - discretization , uniqueness , power law , newtonian fluid , classical mechanics , operator (biology) , physics , inertial frame of reference , momentum (technical analysis) , convection , mathematical analysis , geology , mathematics , mechanics , biochemistry , statistics , chemistry , finance , repressor , transcription factor , economics , gene
SUMMARY Variational principles for the momentum equation with neglected inertial forces are formulated for both Newtonian and power‐law rheologies, and their theoretical functional justification is demonstrated. The existence and uniqueness of the solution are proved, and general gradient optimization techniques prior to discretization are studied. Difficulties with the transformation of the non‐linear problem to a series of linear problems are outlined. To avoid powers of the nabla operator, which appear when the principles are expressed only in terms of velocities, an alternative hybrid variational principle expressed in terms of velocities and stresses is suggested.