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We study the numerical approximation by space-time finite element methods of a coupled hyperbolic-parabolic system modeling, for instance, poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in time and inf-sup stable pairs of finite element spaces for the spatial variables are investigated. Optimal order error estimates are proved for the first-order energy of the system's variables. An important ingredient of the estimates is the control of the coupling terms by a tailored testing strategy. The techniques developed here can be generalized to other families of space-time finite element discretizations and related models. The error estimates are confirmed by numerical experiments, also for higher order piecewise polynomials in space and time. The latter lead to algebraic systems with complex block structure and put a facet of challenge on the design of iterative solvers. An efficient solution technique is referenced. [ABSTRACT FROM AUTHOR]

We develop and study numerically two families of variational time discretization schemes for mixed finite element approximations applied to nonstationary diffusion problems. Continuous and discontinuous approximations of the time variable are encountered. The solution of the arising algebraic block system of equations by a Schur complement technique is described and an efficient preconditioner for the iterative solution process is constructed. The expected higher order rates of convergence are demonstrated in numerical experiments. Moreover, superconvergence properties are verified. Further, the efficiency and stability of the approaches are illustrated for a more sophisticated three-dimensional application of practical interest with discontinuous and anisotropic material properties. [ABSTRACT FROM AUTHOR]

In this work, a flexible higher-order space–time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in poromechanics in which coupled transport with flow, chemical reaction and mechanical response in porous media is considered. Key ingredients are the arbitrary degree discontinuous Galerkin time discretization of the primal and dual problems for the Dual Weighted Residual (DWR) approach, an a posteriori error estimation for the transport problem coupled with flow and its implementation in an advanced software architecture. The error estimate allows the separation of the temporal and spatial discretization error contributions which facilitates the simultaneous adjustment of the time and space mesh. The performance of the approach and its software implementation is studied by numerical convergence examples as well as an example of physical interest for convection-dominated cases. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the new features of the finite element library deal.II, version 9.3. [ABSTRACT FROM AUTHOR]