Galerkin finite element methods for wave problems

Adaptive Galerkin Finite Element Methods for the Wave Equation

This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the...

Discontinuous Galerkin finite element methods for second order hyperbolic problems

In this paper, we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic problems (linear wave equations) based on using spacetime finite element discretizations (for displacements and displacement velocities) with (bilinear) basis functions which are continuous in space and discontinuous in time. We refer to methods of this form as discon...

Galerkin Approximations and Finite Element Methods

Parallel Iterative Discontinuous Galerkin Finite-element Methods

We compare an iterative asynchronous parallel algorithm for the solution of partial diierential equations, with a synchronous algorithm , in terms of termination detection schemes and performance. Both algorithms are based on discontinuous Galerkin nite-element methods, in which the local elements provide a natural decomposition of the problem into computationally-independent sets. We demonstra...

Adaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems

In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...