Convergence order estimates of the local discontinuous Galerkin method for instationary Darcy flow. Issue 4 (31st March 2017)

• Record Type: Journal Article
• Authors: Rupp, Andreas; Knabner, Peter
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 4(2017:Jul.)
• Page Start: 1374
• Page End: 1394
• Publication Date: 2017-03-31
• Subjects: local discontinuous Galerkin method -- instationary Darcy problem -- stability analysis -- error analysis; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22150
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : We present a new a priori stability and convergence analysis for the local discontinuous Galerkin method applied to the instationary Darcy problem formulated on a d ‐dimensional polytope with nonhomogeneous Neumann and Dirichlet boundary conditions. In addition to including a spatially and temporally varying permeability tensor into all estimates, the utilized analysis technique produces a convergence order result for the primary and the flux variables. The only stabilization in the proposed scheme is represented by a penalty term in the primary unknown, and our analysis provides some insights into the role played by this particular choice of stabilization. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1374–1394, 2017