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The convergence rate of approximate solutions for nonlinear scalar conservation laws. (English) Zbl 0765.65092
Let $$\{v^ t(x,t)\}$$ be a $$\text{Lip}^ +$$-stable family of approximate solutions for $$u_ t+f(u)_ x=0$$ with $$C_ 0^ 1$$ initial data. If they are $$\text{Lip}'$$-consistent then they converge to the entropy solution with the rate $${\mathcal O}(\varepsilon)$$. $$L^ p$$ and pointwise error estimates follow.

##### MSC:
 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws
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