Dispersion-based guidance for the temporal and spatial discretization of the one- and two-dimensional finite element solutions to the transient heat equation Original Research Article

Errors associated with the finite element solution to the transient heat equation are examined. These errors arise from the spatial and temporal discretizations chosen and are influenced by the shape of the thermal profile and the properties of the conducting medium. Since these errors alter the rate of heat diffusion, they are termed dispersive. A methodology for evaluating the numerically introduced dispersion is presented. Examples demonstrate that knowledge of the dispersion present in the numerical solution is useful in designing efficient and accurate finite element meshes.