  Traditional finite element approaches are well-known to introduce spurious
oscillations when applied to advection-dominated problems. We explore
alleviation of this issue from the perspective of a generalized finite element
formulation, which enables stabilization through an enrichment process. The
presented work uses solution-tailored enrichments for the numerical solution of
the one-dimensional, unsteady Burgers equation. Mainly, generalizable
exponential and hyperbolic tangent enrichments effectively capture local, steep
boundary layer/shock features. Results show natural alleviation of oscillations
and return smooth numerical solutions over coarse grids. Additionally,
significantly improved error levels are observed compared to Lagrangian finite
element methods.
