Adaptive Discontinuous Galerkin Methods for Eigenvalue Problems Arising in Incompressible Fluid Flows

Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow

The main purpose of this paper is to study the stability and error estimates of the local discontinuous Galerkin (LDG) methods coupled with multi-step implicit-explicit (IMEX) time discretization schemes, for solving time-dependent incompressible fluid flows. We will give theoretical analysis for the Oseen equation, and assess the performance of the schemes for incompressible Navier-Stokes equa...

Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows

In this article we consider the application of goal–oriented mesh adaptation to problems posed on complicated domains which may contain a huge number of local geometrical features, or micro-structures. Here, we exploit the composite variant of the discontinuous Galerkin finite element method based on exploiting finite element meshes consisting of arbitrarily shaped element domains. Adaptive mes...

Benchmark Results for Testing Adaptive Finite Element Eigenvalue Procedures

A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue computations on a collection of benchmark examples. After demonstrating the effectivity of our computed error estimates on a few well-studied examples, we present results for several examples in which the coefficients of the partial-diffe...

Space-time discontinuous Galerkin finite element method for two-fluid flows

A novel numerical method for two-fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relativ...

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows