Research Seminar in Analysis in conjunction with the Colloquium at UMR
meets again in G5 (Rolla Building)
on Thursday, Oct 5, 2000, 3:30 pm.
All interested faculty and students are invited to attend.
High-order mimetic finite difference methods.
By combining the support-operators method with the mapping method, we have derived new mimetic fourth-order accurate discretizations of the divergence, gradient, and Laplacian on nonuniform grids. These finite difference operators mimic the differential and integral identities satisfied by the differential operators. For example, the discrete divergence is the negative of the adjoint of the discrete gradient and consequently the Laplacian is a symmetric negative operator. We analyze the loss of accuracy in the approximations when the grid is rough and include numerical examples demonstrating the effectiveness of the higher order methods on nonuniform grids in one and two dimensions. The analysis and examples are for fourth-order finite difference methods, but the approach can be extended to create approximations of arbitrarily high order.