A new error analysis of characteristics-mixed FEMs for miscible displacement in porous media

The method of characteristics type is especially effective for convection-dominated diffusion problems. Due to the nature of characteristic temporal discretization, the method allows one to use a large time step in many practical computations, while all previous theoretical analyses always required certain restrictions on the time stepsize. Here, we present a new analysis to establish unconditionally optimal error estimates for a modified method of characteristics with a mixed finite element approximation to the miscible displacement problem in ℝ^d (d = 2,3). For this purpose, we introduce a new characteristic time-discrete system. We prove that the L² error bound the characteristic time-discrete systemof the fully discrete method of characteristics to the time-discrete system is τ-independent and the numerical solution is bounded in W^1,∞-norm unconditionally. With the boundedness, optimal error estimates are established in a traditional manner. Numerical results confirm our theoretical analysis and clearly show the unconditional stability. © 2014 Society for Industrial and Applied Mathematics