Combined finite element-finite volume solution of compressible flow

Error Estimates for Barycentric Finite Volumes Combined with Nonconforming Finite Elements Applied to Nonlinear Convection-Diffusion Problems

“…Another possible time discretization which we have applied with success is the inviscid-viscous operator splitting described, e.g., in [6], [13], [14], [15].…”

“…See also [11] or [30].) In [6], [8], [13], [14], [15], we have developed combined finite volume-finite element methods, which exploit advantages of both the above methods. Numerical experiments proved the efficiency and robustness of these methods with respect to the precise resolution of boundary layers and shock capturing.…”

“…In [6], [8], [13], [14], [15] we developed numerical methods for the solution of the high-speed viscous compressible flow in domains with complex geometry. These methods are based on the combination of a finite volume scheme for the discretization of inviscid convective terms and the finite element discretization of viscous terms.…”

A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation

“…Work on a least-squares finite element using a Gartland-type mesh is reported in [21]. Recently, Feistauer et al ( [7,8,9]) proposed and analyzed some semi-implicit and explicit schemes based on combinations of the finite element and finite volume methods for nonlinear timedependent convection-diffusion problems. These methods have been successfully used in solving practical problems.…”

Analysis of a combined barycentric finite volume—nonconforming finite element method for nonlinear convection-diffusion problems

“…In [6], [9], [10], [12] we developed numerical methods for the solution of high-speed viscous compressible flow in domains with complex geometry. These methods are based on the combination of a finite volume scheme for the discretization of inviscid convective terms and the finite element discretization of viscous terms.…”