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We study the local discretization error of Patankar-type Runge-Kutta methodsapplied to semi-discrete PDEs. For a known two-stage Patankar-type scheme thelocal error in PDE sense for linear advection or diffusion is shown to be ofthe maximal order ${\cal O}(\Delta t^3)$ for sufficiently smooth and positiveexact solutions. However, in a test case mimicking a wetting-drying situationas in the context of shallow-water flows, this scheme yields large errors inthe drying region. A more realistic approximation is obtained by a modificationof the Patankar approach incorporating an explicit testing stage into theimplicit trapezoidal rule.

Patankar-Type Runge-Kutta Schemes for Linear PDEs