科研之友
微信
新浪微博
Facebook
分享链接
摘要
We consider an initial value problem for a class of evolution equations incorporating a memory term with a weakly singular kernel bounded by C(t - s)(alpha-1), where 0 < alpha < 1. For the time discretization we apply the discontinuous Galerkin method using piecewise polynomials of degree at most q - 1, for q = 1 or 2. For the space discretization we use continuous piecewise-linear finite elements. The discrete solution satisfies an error bound of order k(q) h(2)l(k), where k and h are the mesh sizes in time and space, respectively, and l(k) = max(1, log k(-1)). In the case q = 2, we prove a higher convergence rate of order k(3) h(2)l(k) at the nodes of the time mesh. Typically, the partial derivatives of the exact solution are singular at t = 0, necessitating the use of non-uniform time steps. We compare our theoretical error bounds with the results of numerical computations.
- 出版日期2009-10
- 单位中国石油大学（北京）
