On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

Discontinuous Galerkin Methods for the Unsteady Compressible Navier-Stokes Equations

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Error Estimates for the Discontinuous Galerkin Methods for Parabolic Equations

We analyze the classical discontinuous Galerkin method for a general parabolic equation. Symmetric error estimates for schemes of arbitrary order are presented. The ideas we develop allow us to relax many assumptions freqently required in previous work. For example, we allow different discrete spaces to be used at each time step and do not require the spatial operator to be self adjoint or inde...

Adjoint-based h-p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid compressible Euler equations. This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest. The converg...

Adjoint-based h-p Adaptive Discontinuous Galerkin Methods for the Compressible Euler Equations

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid compressible Euler equations. This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest. The converg...