A nonlinear Petrov-Galerkin method that minimizes residuals in Lq-type norms is applied to convection-diffusion-reaction equations, numerically demonstrating that over- and undershoots near boundary layers vanish as q tends to 1 on suitable meshes.
Guermond, A finite element technique for solving first-order PDEs in LP , SIAM J
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Eliminating Gibbs Phenomena: A Non-linear Petrov-Galerkin Method for the Convection-Diffusion-Reaction Equation
A nonlinear Petrov-Galerkin method that minimizes residuals in Lq-type norms is applied to convection-diffusion-reaction equations, numerically demonstrating that over- and undershoots near boundary layers vanish as q tends to 1 on suitable meshes.