L. Grubiši´c was supported by the Croatian MZOS Grant Nr. 037- 0372783-2750 "Spectral decompositions—numerical methods and applications" and the bilateral MZOS– NSF Grant "Estimates for finite element approximation error by auxiliary subspace method". A. Mie˛dlar was supported by the DFG Research Center Matheon. J. Ovall was supported by the National Science Foundation under contract DMS-1414365.
Eigenvalues, Nonselfadjoint operators, Spectral theory (Mathematics)
We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection–diffusion–reaction type. These estimates are incorporated as part of an hp-adaptive finite element algorithm for practical spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. Provided experiments demonstrate the efficiency and reliability of our approach.
Giani, Stefano; Grubišić, Luka; Międlar, Agnieszka; and Ovall, Jeffrey S., "Robust Estimates for hp-Adaptive Approximations of Non-Self-Adjoint Eigenvalue Problems" (2015). Mathematics and Statistics Faculty Publications and Presentations. 111.