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An adaptive $$hp$$-version of the finite element method applied to flame propagation problems. (English) Zbl 0901.76037
This paper describes an adaptive $$hp$$-version mesh refinement strategy and its application to the finite element solution of one-dimensional flame propagation problems. The aim is to control the spatial and time discretization errors below a prescribed error tolerance at all time levels. In the algorithm, the optimal time step is first determined in an adaptive manner by considering the variation of the computable error in the reaction zone. Later, the method uses a $$p$$-version refinement till the computable a posteriori error is brought down below the tolerance. Numerical simulations have been carried out for a linear parabolic problem and premixed flame propagation in one-space dimension.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76V05 Reaction effects in flows 80A25 Combustion
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