examples/drivencavity-compatible.py

nelems=12 Number of elements along edge.
degree=2 Polynomial degree for velocity; the pressure space is one degree less.
reynolds=1000 Reynolds number, taking the domain size as characteristic length.

stokes

solve

solving 482 dof system to machine precision using arnoldi solver

residual decreased by 14.5 orders using 0 krylov vectors

residual decreased by 0.7 orders using 1 krylov vectors

solver returned with residual 2e-17

velocity divergence: 1.21e-15

optimize

solve

solving 624 dof system to machine precision using arnoldi solver

residual decreased by 14.8 orders using 0 krylov vectors

residual decreased by 0.3 orders using 1 krylov vectors

solver returned with residual 3e-16

optimum value 2.78e-17

flow.png

navierstokes

newton 0%

solve

solving 482 dof system to tolerance 3e-05 using arnoldi solver

residual decreased by 14.2 orders using 0 krylov vectors

solver returned with residual 2e-16

estimated residual minimum at 44% of update vector

estimated residual minimum at 94% of update vector

update accepted at relaxation 0.43908

newton 2%

solve

solving 482 dof system to tolerance 2e-05 using arnoldi solver

residual decreased by 14.0 orders using 0 krylov vectors

solver returned with residual 2e-16

estimated residual minimum at 63% of update vector

estimated residual minimum at 103% of update vector

update accepted at relaxation 0.26181

newton 2%

solve

solving 482 dof system to tolerance 2e-05 using arnoldi solver

residual decreased by 14.3 orders using 0 krylov vectors

solver returned with residual 9e-17

estimated residual minimum at 166% of update vector

update accepted at relaxation 0.2706

newton 4%

solve

solving 482 dof system to tolerance 2e-05 using arnoldi solver

residual decreased by 14.4 orders using 0 krylov vectors

solver returned with residual 6e-17

estimated residual minimum at 132% of update vector

update accepted at relaxation 0.44991

newton 6%

solve

solving 482 dof system to tolerance 1e-05 using arnoldi solver

residual decreased by 14.1 orders using 0 krylov vectors

solver returned with residual 7e-17

estimated residual minimum at 87% of update vector

update accepted at relaxation 0.59298

newton 8%

solve

solving 482 dof system to tolerance 7e-06 using arnoldi solver

residual decreased by 14.2 orders using 0 krylov vectors

solver returned with residual 4e-17

estimated residual minimum at 172% of update vector

update accepted at relaxation 0.51535

newton 11%

solve

solving 482 dof system to tolerance 4e-06 using arnoldi solver

residual decreased by 14.5 orders using 0 krylov vectors

solver returned with residual 1e-17

estimated residual minimum at 117% of update vector

update accepted at relaxation 0.88528

newton 21%

solve

solving 482 dof system to tolerance 6e-07 using arnoldi solver

residual decreased by 14.8 orders using 0 krylov vectors

solver returned with residual 8e-19

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 50%

solve

solving 482 dof system to tolerance 2e-09 using arnoldi solver

residual decreased by 14.4 orders using 0 krylov vectors

solver returned with residual 7e-21

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 94%

solve

solving 482 dof system to tolerance 3e-13 using arnoldi solver

residual decreased by 14.9 orders using 0 krylov vectors

solver returned with residual 4e-25

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 10 steps to residual 1.3e-17

velocity divergence: 9.50e-16

optimize

solve

solving 624 dof system to machine precision using arnoldi solver

residual decreased by 14.6 orders using 0 krylov vectors

residual decreased by 0.3 orders using 1 krylov vectors

solver returned with residual 5e-16

optimum value 1.39e-17

flow.png