Mimetic Finite Difference Methods for Partial Differential Equations and Discrete Vector and Tensor Analysis
Tuesday, May 11, 2004 - 1:30pm - 2:20pm
In past 10 years we have developed new high-quality, mimetic finite-difference methods based on discrete analog of vector and tensor analysis (DVTA). The basis of DVTA is the design of discrete operators that preserve certain essential properties of, and relationships between, the corresponding analytic operators. The DVTA is the basis for new techniques for large-scale numerical simulations approximating the solution of partial differential equations (PDEs). The new methods provide a significant extension of the well known and useful finite volume methods and are designed to more faithfully represent important properties of physical processes and the continuum mathematical models of such processes. Algorithms based on these techniques are used for modeling high-speed flows, porous media flows, diffusion processes, and electromagnetic problems. In this presentation we will describe DVTA and demonstrate how it can be used to construct high-quality finite-difference methods for PDEs.