A comparison between two solution techniques to solve the equations of linear isostasy

In this paper we compare two models to compute the isostatic response of the Earths lithosphere to an external load. The lithosphere is modeled as a linear elastic solid. The two models differ in the mathematical formulation of the problem, their applicability in the incompressible limit, the choice of the finite elements used for discretization, and the solution strategy for the arising algebraic problem. The efficiency and accuracy of both models are compared via extensive numerical experiments in 2D and 3D.

[1]  J. Mitrovica,et al.  Glacial isostatic adjustment on a rotating earth , 2001 .

[2]  Gene H. Golub,et al.  Numerical solution of saddle point problems , 2005, Acta Numerica.

[3]  Z. Martinec.  Spectral–finite element approach to three‐dimensional viscoelastic relaxation in a spherical earth , 2000 .

[4]  J. Mitrovica,et al.  Postglacial sea-level change on a rotating Earth , 1998 .

[5]  Maya Neytcheva,et al.  An Agglomerate Multilevel Preconditioner for Linear Isostasy Saddle Point Problems , 2005, LSSC.

[6]  P. Johnston.  The effect of spatially non‐uniform water loads on prediction of sea‐level change , 1993 .

[7]  Björn Lund,et al.  A comparison between two approaches to solve the equations of linear isostasy , 2006 .

[8]  Owe Axelsson,et al.  On iterative solvers in structural mechanics; separate displacement orderings and mixed variable methods , 1999 .

[9]  W. Peltier.  The impulse response of a Maxwell Earth , 1974 .

[10]  W. Wal,et al.  Postglacial sealevels on a spherical, self-gravitating viscoelastic earth: effects of lateral viscosity variations in the upper mantle on the inference of viscosity contrasts in the lower mantle , 2003 .

[11]  Detlef Wolf,et al.  Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models , 2003 .

[12]  D. Komatitsch,et al.  Glacial isostatic adjustment on 3‐D Earth models: a finite‐volume formulation , 2005 .

[13]  M. Neytcheva,et al.  Numerical simulations of glacial rebound using preconditioned iterative solution methods , 2005 .

[14]  Patrick Wu,et al.  Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress , 2004 .

[15]  F. Brezzi,et al.  A discourse on the stability conditions for mixed finite element formulations , 1990 .

[16]  D. Wolf.  Viscoelastodynamics of a stratified, compressible planet: incremental field equations and short- and long-time asymptotes , 1991 .

[17]  W. Peltier,et al.  Viscous gravitational relaxation , 1982 .

[18]  J. Wahr,et al.  The viscoelastic relaxation of a realistically stratified earth, and a further analysis of postglacial rebound , 1995 .