with finite difference and finite element methods, in which the resolution of the grid needs to be sufficiently large in order to avoid numerical instabilities when the P´ eclet number is large O˜ nate (2000). The debiasing estimates are more variable in time taken to obtain an estimate, with the most expen- sive estimate taking 113 seconds in these experiments. This demonstrates that extreme draws for the halting value can add a significant amount of computational expense Now consider the following 2D PDE system, with initial and boundary conditions Here we choose 23 k ( x ) = exp ( 1 2 x$_{(1)}$x$_{(2)}$ ) . u ( x x, t ) = x$_{(2)}$, x$_{(1)}$ = 1 , x$_{(2)}$ ∈ [0 , 1] , t ≥ 0 , u ( x x, t ) = 0 , x$_{(1)}$ = 0 , x$_{(2)}$ ∈ [0 , 1] , t ≥ 0 , u ( x x, t ) = x$_{(1)}$, x$_{(1)}$ ∈ [0 , 1] , x$_{(2)}$ = 1 , t ≥ 0 , u ( x x, t ) = 0 , x$_{(1)}$ ∈ [0 , 1] , x$_{(2)}$ = 0 , t ≥ 0 , u ( x x, 0) = x$_{(1)}$x$_{(2)}$, x$_{(1)}$ ∈ [0 , 1] , x$_{(2)}$ ∈ [0 , 1] , ∂u ( x x, t ) ∂t = ∇ k ( x ) · ∇ u ( x x, t ) + 1 2 ∇ $^{2}$u ( x x, t ) , t ≥ 0 , x x ∈ [0 , 1] × [0 , 1] , 5.2. 2D Example