Equal higher order analysis of an unfitted discontinuous Galerkin method for Stokes flow systems

by   Georgios Katsouleas, et al.

In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds, firstly the advantages of a piece-wise discontinuous high–order accurate approximation and secondly the advantages of an unfitted to the true geometry grid around possibly complex objects and/or geometrical deformations. Utilizing a fictitious domain framework, the physical domain of interest is embedded in an unfitted background mesh and the geometrically unfitted discretization is built upon symmetric interior penalty discontinuous Galerkin formulation. A fully stabilized frame is required for equal order finite elements, both –proper for higher-order– pressure Poisson stabilization in the bulk of the domain, as well as boundary zone velocity and pressure ghost penalty terms. The present contribution should prove valuable in engineering applications where special emphasis is placed on the optimal effective approximation attaining much smaller relative errors in coarser meshes. Inf-sup stability, the optimal order of convergence, and the stabilization parameters dependency are investigated. Our analysis of the stability properties of the proposed scheme reveals that a delicate scaling of the stabilization parameters is required for the equal higher-order case. This is also supported by numerical evidence from test experiments. Additionally, a geometrically robust estimate for the condition number of the stiffness matrix is provided. Numerical examples illustrate the implementation of the method and verify the theoretical findings.


page 3

page 6


Higher-order discontinuous Galerkin time discretizations the evolutionary Navier–Stokes equations

Discontinuous Galerkin methods of higher order are applied as temporal d...

An embedded--hybridized discontinuous Galerkin method for the coupled Stokes--Darcy system

We introduce an embedded--hybridized discontinuous Galerkin (EDG--HDG) m...

Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated

We study two techniques for correcting the geometrical error associated ...

Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems

A hybridizable discontinuous Galerkin (HDG) formulation of the linearize...

A pressure-stabilized projection Lagrange–Galerkin scheme for the transient Oseen problem

We propose and analyze a pressure-stabilized projection Lagrange–Galerki...

Parameter-free implementation of the quadratic C^0 interior penalty method for the biharmonic equation

The symmetric C^0 interior penalty method is one of the most popular dis...

Please sign up or login with your details

Forgot password? Click here to reset