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Basic Iterative Algorithms of Numerical Linear Algebra as Building Blocks for Hybrid Adaptive Finite Element Methods

Implementation and analysis of modern adaptive finite element procedures for the computation of eigenvalues of partial differential operators requires a fine interplay of techniques from approximation theory, analysis, linear algebra and discrete mathematics. Often computational effort spent on doing linear algebra tasks far outweighs the cumulative effort in performing other algorithmic steps. Yet, utilization of linear algebra is seldom optimized as an integral part the adaptive mesh refinement loop Compute -> Estimate -> Mark - > Refine. We extend our earlier analysis of the self-adjoint eigenvalue problem to a non-self adjoint convection diffusion type operator.

adaptive finite element methods; convergence enhancement; non self-adjoint problems

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