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Title: An A Posteriori KAM Theorem for Whiskered Tori in Hamiltonian Partial Differential Equations with Applications to some Ill-Posed Equations
Award ID(s):
1800241
NSF-PAR ID:
10094862
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Archive for Rational Mechanics and Analysis
Volume:
231
Issue:
2
ISSN:
0003-9527
Page Range / eLocation ID:
971 to 1044
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  2. Abstract We propose a uniform block-diagonal preconditioner for condensed $H$(div)-conforming hybridizable discontinuous Galerkin schemes for parameter-dependent saddle point problems, including the generalized Stokes equations and the linear elasticity equations. An optimal preconditioner is obtained for the stiffness matrix on the global velocity/displacement space via the auxiliary space preconditioning technique (Xu (1994) The Auxiliary Space Method and Optimal Multigrid Preconditioning Techniques for Unstructured Grids, vol. 56. International GAMM-Workshop on Multi-level Methods (Meisdorf), pp. 215–235). A spectrally equivalent approximation to the Schur complement on the element-wise constant pressure space is also constructed, and an explicit computable exact inverse is obtained via the Woodbury matrix identity. Finally, the numerical results verify the robustness of our proposed preconditioner with respect to model parameters and mesh size. 
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