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Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation. (English) Zbl 0701.65097

Summary: We present the numerical analysis of the classical thermal-diffusional model describing a curved premixed flame propagating in a rectangular infinite tube. The adaptive moving mesh procedure used to numerically solve this problem leads to a system of non-linear integro-differential reaction-diffusion equations. We mathematically prove the existence and uniqueness of a solution to this problem and show the convergence of the numerical approximation. A particular feature of the analysis is that the estimates of the global numerical error not only depend on the time step and mesh spacing \(\Delta\) t, \(\Delta\) x, \(\Delta\) y, but also of the size of the computational domain.

MSC:

65R20 Numerical methods for integral equations
80A20 Heat and mass transfer, heat flow (MSC2010)
45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
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References:

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