| This dissertation addresses the issue of a-posteriori estimation of the error in the finite element solution, both in a non-guaranteed, and guaranteed sense, for steady-state and transient linear heat-conduction problems in curvilinear domains, and domains with subregions of high material orthotropy. A thorough computer analysis of the validity of various a-posteriori error estimators found in the literature for problems involving singularities and subregions of high material orthotropy is given. Algorithms to compute reliable upper and lower bounds with the optimal constants for the error in the energy norm, and the quantity of interest are given and analysed for problems occurring in practical computation.; The techniques of a-posteriori error estimation developed for the elliptic case are then utilized for the parabolic case to obtain the a-posteriori estimates of the error in both, the time and space discretization. A computer analysis of the validity of the estimators for the transient linear heat-conduction problems are given for domains occurring in practical computation. |
