15- https://doi.org/10.1007/s10915-015-0004-9
Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
- Mar 24, 2015
- Journal of Scientific Computing
- Morrakot Khebchareon +2 more
We formulate and analyze new methods for the solution of a partial integrodifferential equation with a positive-type memory term. These methods combine the finite element Galerkin (FEG) method for the spatial discretization with alternating direction implicit (ADI) methods based on the Crank---Nicolson (CN) method and the second order backward differentiation formula for the time stepping. The ADI FEG methods are proved to be of optimal accuracy in time and in the $$L^2$$L2 norm in space. Furthermore, the analysis is extended to include an ADI CN FEG method with a graded mesh in time for problems with a nonsmooth kernel. Numerical results confirm the predicted convergence rates and also exhibit optimal spatial accuracy in the $$L^{\infty }$$L? norm.
- # Finite Element Galerkin Method
- # Alternating Direction Implicit
- # Nonsmooth Kernel
- # Norm In Space
- # Finite Element Galerkin
- # Galerkin Method For Discretization
- # Accuracy In Time
- # Optimal Accuracy
- # L2 Norm
- # Crank---Nicolson
