Two new error estimates of a fully discrete primal-dual mixed finite element scheme for parabolic equations in any space dimension
A fully discrete implicit scheme is considered, in which the discretization in space is performed using the Primal-Dual Mixed Finite Element Method (PDMFEM) as an approximation in space for the non-stationary heat equation as a model of parabolic equations in any space dimension. The time discretization is performed using a uniform mesh. The existence and uniqueness of the discrete solution are shown. The convergence results which state the optimal estimate for the error are proved. The organization of this paper is as follows. In Section 1, the problem to be solved, preliminaries, formulation of the PDMFE scheme, and aim of this paper are given. In Section 2, the main convergence results in a general setting of finite element spaces are studied. Section 3 is devoted to the application of the results of Section 2 to the particular case when the mixed finite element spaces are defined by the known Raviart-Thomas spaces of order l. In Section 5, the authors summarize the results of the paper and sketch some perspectives to work on in the near future.
scientific article; zbMATH DE number 7383832
scientific article