eXtended hybridizable discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces

Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Cites Work

To CG or to HDG: a comparative study in 3D
Hybridizable discontinuous Galerkin method (HDG) for Stokes interface flow
To CG or to HDG: A comparative study
Numerical and computational efficiency of solvers for two-phase problems
A comparison of HDG methods for Stokes flow
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations
Studied X-FEM enrichment to handle material interfaces with higher order finite element
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
Hybridizable discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations
eXtended hybridizable discontinuous Galerkin with Heaviside enrichment for heat bimaterial problems
Calculation of two-phase Navier-Stokes flows using phase-field modeling
An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
Comparison of high-order continuous and hybridizable discontinuous Galerkin methods for incompressible fluid flow problems
Higher-order meshing of implicit geometries. I: Integration and interpolation in cut elements
Extended hybridizable discontinous Galerkin (X-HDG) for void problems
A cut finite element method for a Stokes interface problem
Analysis of an XFEM Discretization for Stokes Interface Problems
Conditions for superconvergence of HDG methods for second-order elliptic problems
A high-order hybridizable discontinuous Galerkin method for elliptic interface problems
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
The extended/generalized finite element method: An overview of the method and its applications
Analysis of HDG methods for Stokes flow
IMMERSED BOUNDARY METHODS
Higher-order XFEM for curved strong and weak discontinuities
A finite element method for crack growth without remeshing
High‐order continuous and discontinuous Galerkin methods for wave problems
Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem