Hofreither, C. \(L_{2}\) error estimates for a nonstandard finite element method on polyhedral meshes. (English) Zbl 1222.65119 J. Numer. Math. 19, No. 1, 27-39 (2011). The paper deals with the boundary element method-based finite element method (BEM-based FEM) approach which employs locally partial differential equation (PDE)-harmonic trial functions, i.e. trial functions which satisfy the PDE locally on each element and uses boundary element techniques to assemble the element stiffness matrices. The author shows an alternate approach to the analysis via a mixed formulation having both Dirichlet and Neumann traces as its unknowns. The method is able to treat general polyhedral meshes. The author recovers mesh-independent error estimates in the \(H^1\)-norm as well as previously unavailable \(L_2\) error estimates. Reviewer: Adrian Carabineanu (Bucureşti) Cited in 1 ReviewCited in 13 Documents MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:polyhedral meshes; BEM-based FEM; mixed formulation; error estimates; boundary element method; error estimates PDFBibTeX XMLCite \textit{C. Hofreither}, J. Numer. Math. 19, No. 1, 27--39 (2011; Zbl 1222.65119) Full Text: DOI References: [1] DOI: 10.4171/ZAA/1170 · Zbl 1057.26011 [2] DOI: 10.1137/040613950 · Zbl 1108.65102 [3] Copeland D. M., Int. J. Appl. Math. Comput. Sci. 5 (1) pp 60– (2009) [4] DOI: 10.1016/j.cma.2004.07.017 · Zbl 1093.76034 [5] DOI: 10.1007/s00791-006-0017-x · Zbl 1511.92031 [6] Hofreither C., Electron. Trans. Numer. Anal. 37 pp 413– (2010) [7] DOI: 10.1007/BF02392869 · Zbl 0489.30017 [8] DOI: 10.1515/156939506779874617 · Zbl 1122.65112 [9] DOI: 10.1007/s10596-004-3771-1 · Zbl 1088.76046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.