[dune-pdelab] Sign convention for linear problems

Oliver Sander oliver.sander at tu-dresden.de
Wed May 24 10:00:21 CEST 2017


Dear pdelab team,

I have found out that the ConvectionDiffusionFEM LocalOperator assembles
the residual in the form

  r(x) = Ax - b.

Consequently, the GridOperator::jacobian method gives me the stiffness matrix,
and GridOperator::residual gives me the negative(!) load vector.

Now I am wondering: ConvectionDiffusionFEM may just as well return the residual as

  r(x) = b - Ax.

For nonlinear problem this sign choice doesn't matter at all, but for linear ones
it matters a little bit.  Is there a general rule whether LocalOperators for linear
problems should compute Ax-b rather than b-Ax?  Or is each LocalOperator free to
pick its own sign convention?  Is this documented anywhere?

Thanks for your help,
Oliver

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