A transport corrected finite element advection scheme

A new scheme for horizontal advection in a finite element ocean model is presented. It is based on a pointwise flux-correcting method, and efficiency is kept high by exploiting nodal quadrature in combination with two meshes having linear and quadratic basis functions. The new advection scheme reduces over- and undershooting and instabilities found with the original scheme used in the ocean model, and it is thus possible to apply smaller and more reasonable mixing coefficients and keep sharper gradients with the new scheme. Tests show that the ocean model with the new scheme doubles the run time, though this might be outstripped by the possibility to apply a larger time step.