Computer Methods in Applied Mechanics and Engineering
Journal of Computational Physics
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Local Discontinuous Galerkin Methods for the Stokes System
SIAM Journal on Numerical Analysis
A compiler for variational forms
ACM Transactions on Mathematical Software (TOMS)
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Journal of Scientific Computing
ACM Transactions on Mathematical Software (TOMS)
Automated Code Generation for Discontinuous Galerkin Methods
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
SIAM Journal on Scientific Computing
DOLFIN: Automated finite element computing
ACM Transactions on Mathematical Software (TOMS)
Analysis of an Interface Stabilized Finite Element Method: The Advection-Diffusion-Reaction Equation
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
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A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations.