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In this paper we extend output-based error estimation to recently-developed active-ux schemes. We use the active ux method for its ability to eciently incorporate third-order accuracy for convection-dominated problems. The error estimation requires a discrete unsteady adjoint solution, for which we provide implementation details and verication demonstrations. We also introduce a localization strategy in which the adjoint-weighted residual inner product is split into contributions from various elements and nodes to create an adaptive indicator. We demonstrate the ability of these adaptative indicators to drive mesh renement in two-dimensional advection, and we show favorable comparisons to uniform mesh renement.

Adjoint-Based Error Estimation and Mesh Adaptation for the Active Flux Method