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The paper of Cockburn and Shu [1] explains this. If the solution is $$ u_h(x) = u_i + u_{xi} \phi(x), \qquad \phi(x) = \frac{x - x_i}{\Delta x/2} $$ Then the limiter is $$ u_{xi} = minmod(u_{xi}, u_i - u_{i-1}, u_{i+1}-u_i) $$ Does your solution representation look as in the first equation above ? Also, the solution with normalised Legendre basis will look ...


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