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Moving mesh method with local time step refinement for blow-up problems. (English) Zbl 1130.65092
Summary: The dynamical moving mesh method is merged with the local time stepping technique and the new method is applied for blow-up problems. It has some benefit in approximating an accurate blow-up time by starting at any positive initial time (\(t_{0}> 0)\).
Our numerical experiment shows that without applying the local time stepping method, the wrong blow-up time will be obtained, if the equation integrates from \(t_{0}> 0\).

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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