Locally conservative discontinuous PetrovGalerkin finite elements for fluid problems
We develop a locally conservative formulation of the discontinuous PetrovGalerkin finite element method (DPG) for convectiondiffusion type problems using Lagrange multipliers to exactly enforce conservation over each element. We provide a proof of convergence as well as extensive numerical experiments showing that the method is indeed locally conservative. We also show that standard DPG, while not guaranteed to be conservative, is nearly conservative for many of the benchmarks considered. The new method preserves many of the attractive features of DPG, but turns the normally symmetric positive-definite DPG system into a saddle point problem.
local conservation discontinuous petrovgalerkin convection-diffusion stokes flow least squares minimum residual higher order adaptive mesh refinement