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Iterative solution of the stream function–vorticity equations using a multigrid solver with finite elements. (English) Zbl 0777.76049

Summary: The solution of the stream function–vorticity equations is developed using a multigrid method to improve efficiency in a finite-element \(p\)- method. The equations are discretized using 2-\(D\) Lagrange finite elements (linear, quadratic and cubic) and solved in iteratively decoupled form using successive approximation and continuation methods. The comparative performance of several multigrid and direct matrix solvers is investigated with respect to convergence characteristics and time performance on the Cray \(Y\)-\(MP\).

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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References:

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