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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.

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
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