The thesis presents a comprehensive study of a posteriori error estimation in the adaptive solution to some classical elliptic partial differential equations. Several new error estimators are proposed for diffusion problems with discontinuous coefficients and for convection-reaction-diffusion problems with dominated convection/reaction. The robustness of the new estimators is justified theoretically. Extensive numerical results demonstrate the robustness of the new estimators for challenging problems and indicate that, compared to the well-known residual-type estimators, the new estimators are much more accurate.
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/8304383 |
| Date | 13 August 2019 |
| Creators | Difeng Cai (5929550) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/ROBUST_AND_EXPLICIT_A_POSTERIORI_ERROR_ESTIMATION_TECHNIQUES_IN_ADAPTIVE_FINITE_ELEMENT_METHOD/8304383 |
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