Log In Sign Up

Convergence of a continuous Galerkin method for mixed hyperbolic-parabolic systems

by   Markus Bause, et al.

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modelling poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in space and time with inf-sup stable pairs of finite elements for the spatial approximation of the unknowns are investigated. Optimal order error estimates of energy-type are proven. Superconvergence at the time nodes is addressed briefly. The error analysis can be extended to discontinuous and enriched Galerkin space discretizations. The error estimates are confirmed by numerical experiments.


page 1

page 2

page 3

page 4


Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations

In this paper we study the finite element approximation of systems of se...

Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation

In this paper we present a Local Fourier Analysis of a space-time multig...

Continuous time integration for changing time systems

We consider variational time integration using continuous Galerkin Petro...

C^1-conforming variational discretization of the biharmonic wave equation

Biharmonic wave equations are of importance to various applications incl...

Convergence analysis of some tent-based schemes for linear hyperbolic systems

Finite element methods for symmetric linear hyperbolic systems using uns...

Structure aware Runge-Kutta time stepping for spacetime tents

We introduce a new class of Runge-Kutta type methods suitable for time s...

New analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media

Analysis of Galerkin-mixed FEMs for incompressible miscible flow in poro...