| Author | Slimane Adjerid, Ivo Babuska and Joseph E. Flaherty |
|---|---|
| Title | A Posteriori Error Estimation for the Finite Element Method-of-Lines Solution of Parabolic Problems |
| Year | 1997 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 21 |
| Pages | 728-746 |
| Issue | 2 |
| Publisher | Society for Industrial and Applied Mathematics |
| Abstract | Babuska and Yu constructed a posteriori estimates for finite element discretization errors of linear elliptic problems utilizing a dichotomy principal stating that the errors of odd-order approximations arise near element edges as mesh spacing decreases while those of even-order approximations arise in element interiors. We construct similar a posteriori estimates for the spatial errors of finite element method-of-lines solutions of linear parabolic partial differential equations on square-element meshes. Error estimates computed in this manner are proven to be asymptotically correct; thus, they converge in strain energy under mesh refinement at the same rate as the actual errors. |
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