Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, use of mixed FEMs/CG/DG, LBM and lax milligram for stability, descrete stability for different time discritizaition schemes...
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$\begingroup$ Since nobody has replied, don't the books by Brenner and Scott or the five or six series by Oden and Carey have what you want? $\endgroup$– NNNCommented Jun 15 at 3:46
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I would suggest the books below:
- Susanne C. Brenner , L. Ridgway Scott - The Mathematical Theory of Finite Element Methods
- Daniele Boffi , Franco Brezzi , Michel Fortin - Mixed Finite Element Methods and Applications
- Elman, H Silvester, D Wathen, A - Finite Elements and Fast Iterative Solvers
- Daniele Antonio Di Pietro , Alexandre Ern - Mathematical Aspects of Discontinuous Galerkin Methods
- Béatrice Rivière - Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation
- Jan S. Hesthaven , Tim Warburton - Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
- Peter Wriggers - Nonlinear Finite Element Methods
These should cover most of the asker's requests, if anyone has suggestions I am happy to evaluate and add to the list.
answered Jun 15 at 4:35
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4$\begingroup$ Great list. I would also add Wriggers as a reference specifically on nonlinear problems. $\endgroup$ Commented Jun 17 at 7:50
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1$\begingroup$ Nonlinear Finite Elements by Wriggers, definitely a great suggestion. Thank you! :) $\endgroup$ Commented Jun 18 at 8:06