2015/04/17 by Markus Bause, Bause, Markus, Florin A. Radu +3
Computer Science · Decision Sciences · Engineering · #65N12 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1504.04491
openalex publication_date 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Variational time discretization schemes are getting of increasing importance\nfor the accurate numerical approximation of transient phenomena. The\napplicability and value of mixed finite element methods (MFEM) in space for\nsimulating transport processes have been demonstrated in a wide class of works.\nWe consider a family of continuous Galerkin-Petrov time discretization schemes\nthat is combined with a mixed finite element (MFE) approximation of the spatial\nvariables. The existence and uniqueness of the semidiscrete approximation and\nof the fully discrete solution are established. For this, the\nBanach-Ne vcas-Babu vska theorem is applied in a non-standard way. Error\nestimates with explicit rates of convergence are proved for the scalar and\nvector-valued variable. An optimal order estimate in space and time is proved\nby duality techniques for the scalar variable. The convergence rates are\nanalyzed and illustrated by numerical experiments, also on stochastically\nperturbed meshes.\n