  Higher-order numerical methods are used to find accurate numerical solutions
to hyperbolic partial differential equations and equations of transport type.
Limiting is required to either converge to the correct type of solution or to
adhere to physically motivated local maximum principles. Less restrictive
limiting procedures are required so as to not severely decrease the accuracy.
  In this paper, we develop an existing slope limiter framework, to achieve
different local boundedness principles for higher-order schemes on unstructured
meshes. Quadrature points contributing to numerical fluxes can be limited based
on face defined maximum principles, and the resulting cell mean at the next
timestep can satisfy a cell mean maximum principle but with less limiting. We
demonstrate the practical application of the introduced framework to a
second-order finite volume scheme as well as a fourth-order finite volume
scheme, in the context of the advection equation.
