A finite volume scheme for solving elliptic boundary value problems on composite grids

Abstract

. (1998). A finite volume scheme for solving elliptic boundary value problems on composite grids. (RANA : reports on applied and numerical analysis; Vol. 9804). Eindhoven: Technische Universiteit Eindhoven. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Local defect correction with different grid types

“…Using definitions (39) and (40) we obtain 2) h uhlfl" + h uhlflJ: = h rui" + h uhlfl;;· Now it follows from (26), (27) that (Uh, ui,,) satisfies (31 and (32).…”

“…It is an iterative procedure which not just combines the solutions on the two grids but also improves the quality of the composite solution by providing information exchange between the grids. LDC was extensively analysed for the Poisson equation when cartesian coordinates are used for both global and local problems, ef [2], [4], see Figure 2a.…”

Local defect correction in numerical simulation of surface remelting

“…The method is combined with finite volume discretizations in [4] and with finite elements in [19]. So-called high order compact difference schemes can be used in an LDC technique too [16].…”

Analysis of local defect correction and high-order compact finite differences

“…The LDC method is combined with finite volume discretizations in [3,4,24]. An application of the LDC algorithm in a finite volume context was presented in [17] for numerical simulations of the flow and heat transfer in a glass tank.…”