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On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes. (English) Zbl 1343.65116
The authors discuss the advantage of choosing the small parameter $$\varepsilon$$ in weighted essentially non-oscillatory (WENO) and CWENO boundary value reconstruction procedures of third order on nonuniform meshes in the setting of finite volume schemes. The current work shows that choosing $$\varepsilon$$ as a function of the local mesh size allows one to recover the optimal error of convergence even close to local extrema of the function being reconstructed and in general provides a much more regular pattern of error decay.

##### MSC:
 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
AMRCLAW
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