On conservation and dual consistency for summation-by-parts based approximations of parabolic problems

• We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In, it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Publication and Content Type

vet (subject category)

rap (subject category)