Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)

Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension

under review
  • We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $d \geq 2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity.

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Author:Martin Heida, Alexander Sikorski, Marcus Weber
Document Type:Article
Parent Title (English):SIAM Journal on Numerical Analysis
Year of first publication:2022
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.