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Intro Racines carrées Collocation mixte Tests numériques Joulin Chaleur Couplage Couplage simplifié Collocation mixte • Integrate the equation (10) with the fractional integrator I β (11) : u (t) − u0 = I β (Φ (u (•) , t)), t ≥ 0. (12) • Low order (P1Q0) mixed collocation method : choose a discrete state u h (•) satisfying u h ∈ P h 1 a flux f h ≃ Φ (u (•) ,t) according to the condition f h ∈ Q h 0 . • Write the equation (12) at the grid points jh (j ∈ N) : , j ∈ N . (13) u h β (jh) − u0 = I f h (•) , jh
Intro Racines carrées Collocation mixte Tests numériques Joulin Chaleur Couplage Couplage simplifié Collocation mixte (ii) • Mean value of the approached flux f h (•) : equal to the mean value of the exact flux in each element : (j+1)h f h (θ) dθ ≡ (j+1)h Φ u h (θ),θ dθ . (14) jh • ”Projection step” on the discrete space Q h 0 : f h j+ 1 2 = 1 0 jh Φ u h j (1 − θ) + θuh j+1 , jh + θh dθ , j ∈ N . (15)
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f. dubois - Laboratoire de Mathématiques et de leurs Applications ...

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