Linearly implicit approximations of diffusive relaxation systems
This paper deals with the combination of relaxation systems with implicit approximations and its theoretical and numerical stability analysis. The author introduces diffusiv relaxation systems for the linear and nonlinear model and presents a discrete approximation of the linear one. This approach is extended by first- and second-order schemes for the nonlinear case using a linearly implicit method. The scheme is implicit for the relaxation system except for the nonlinear source-term where a suitable linearization technique is used, based on a certain correction term. Several theoretical stability estimates under certain conditions (a constant correction term) are provided for the first- and second-order scheme. Furthermore, some numerical testcases are carried out which confirm the theoretical results and yield good performance also in case of the non-constant correction.
scientific article; zbMATH DE number 6175227
scientific article