Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)
  • search hit 3 of 6
Back to Result List

A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces

Please always quote using this URN: urn:nbn:de:0297-zib-8996
  • We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Metadaten
Author:Michael Oevermann, Rupert Klein
Document Type:ZIB-Report
Tag:Poisson equation; ariable and discontinuous coefficients; discontinuous solution; embedded interface; finite volume methods
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J25 Boundary value problems for second-order elliptic equations
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:2006/02/13
Series (Serial Number):ZIB-Report (06-05)
ZIB-Reportnumber:06-05
Published in:Appeared in: J. Comput. Phys., 219, 749--769, (2006)
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.