Abstract

This chapter summarizes the development of a new class of algorithms using Parallel Adaptive hpFinite Elements for the analysis of Stokesian Flows. With parallel computing, these methods reduce computational costs associated with realistic finite element approximations. The chapter introduces the Stokes problem, its finite element formulation, and the appropriate function spaces necessary for a description of the various algorithms used in the solution process. It describes a simple adaptive strategy for producing good hpmeshes. The adaptive strategy comprises of three steps: selecting an intermediate error level between the initial mesh error and the final target mesh, and estimating different parameters; keeping polynomial orders PK constant; and keeping grid size constant and changing the local polynomial orders. The chapter also discusses a construction of compatible approximation spaces for the velocity and pressure spaces. It reviews a recursive load based bisection type mesh partitioning strategy. It describes a domain decomposition type solver for such problems.

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