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\(L_{2}\) error estimates for a nonstandard finite element method on polyhedral meshes. (English) Zbl 1222.65119

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.

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
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References:

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