In:
Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-11
Abstract:
A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇ · ( a ( x , t ) ∇ u ) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H ( d i v ; Ω ) space and the hyperbolic part d ( x )( ∂ u / ∂ t )+ c ( x , t ) · ∇ u is handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L 2 - and H 1 -norms for the scalar unknown u and a priori error estimates in ( L 2 ) 2 -norm for its gradient λ and its flux σ (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.
Type of Medium:
Online Resource
ISSN:
1110-757X
,
1687-0042
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2013
detail.hit.zdb_id:
2578385-3
SSG:
17,1
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