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A lattice Boltzmann model for elliptic equations with variable coefficient. (English) Zbl 1308.35101

Summary: A lattice Boltzmann model is proposed to solve elliptic equations with variable coefficient. Compared with the previous model, the present model is a more effective solver to the ellipse equation with variable coefficient, and the ellipse equation is exactly recovered to order \(O(\epsilon^2)\). The relaxation time \(\tau\) is not fixed and is determined by the coefficient of the equation. The limited numerical results show that the present model is valid for ellipse equations.

MSC:

35J61 Semilinear elliptic equations
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