Name
Title | ||
|---|---|---|
Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s10915-015-0004-9 | Journal of Scientific Computing |
Keywords | Field | DocType |
Partial integrodifferential equation, Positive-type memory term, Finite element Galerkin method, Alternating direction implicit methods, Optimal error estimates, Smooth and nonsmooth kernels, 65M60, 65M12, 65M15 | Kernel (linear algebra),Convergence (routing),Alternating direction implicit method,Discretization,Mathematical optimization,Mathematical analysis,Galerkin method,Finite element method,Backward differentiation formula,Evolution equation,Mathematics | Journal |
Volume | Issue | ISSN |
65 | 3 | 1573-7691 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Morrakot Khebchareon | 1 | 0 | 0.68 |
| Amiya Kumar Pani | 2 | 30 | 4.02 |
| Graeme Fairweather | 3 | 165 | 40.42 |