College of Liberal Arts & Sciences
Mathematics Colloquium - Hailiang Liu
Abstract:
Hyperbolic problems arise in many applications, and considerable amount of literature is available on accurate numerical methods to solve them. In this talk I shall review the alternating evolution (AE) methods for a set of PDEs, including hyperbolic conservation laws, Hamilton-Jacobi equations, and convection-diffusion equations. The AE schemes (finite volume, finite difference, or discontinuous Galerkin) are based on an alternating evolution system for each equation in question, and therefore no numerical flux (or Hamiltonian) is needed in the scheme formulation. Optimal error estimates for AEDG schemes to linear convection-diffusion equations are recently established. Numerical results are reported to illustrate the capacity of some algorithms.