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Convergence of time-space adaptive algorithms for nonlinear conservation laws. (English) Zbl 1273.65119
The authors, combining the multiresolution analysis, the finite volume methodology and advanced tools from functional analysis, construct two adaptive explicit finite volume schemes for scalar nonlinear conservation laws. The first scheme uses a global time step and the second one is the local time-stepping strategy. In both cases the convergence in the weak sense of approximate solutions towards the unique entropy solution of the continuous problem is proved. Numerical tests for the Burgers equation with various initial conditions are presented.
Reviewer: S. Burys (Kraków)
MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M08 Finite volume 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
35Q53 KdV equations (Korteweg-de Vries equations)
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