A combined linear and nonlinear stabilization for continuous Galerkin finite elements on the transport equation yields localized a priori error bounds of order O(h^{k+1/2}) in the final-time L2 norm under local regularity assumptions.
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Local error estimates for a finite element method combining linear and nonlinear stabilization for the linear hyperbolic transport equation
A combined linear and nonlinear stabilization for continuous Galerkin finite elements on the transport equation yields localized a priori error bounds of order O(h^{k+1/2}) in the final-time L2 norm under local regularity assumptions.