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Analysis of dual consistency for discontinuous Galerkin discretizations of source terms. (English) Zbl 1203.65258
The authors are concerned with the study of the effect of dual consistency on a discontinuous Galerkin discretization of the solution and the solution gradient dependent source terms. Dual consistency provides a connection between the continuous and discrete dual problems. Starting from this dual inconsistent scheme a dual consistent discretization is developed. Furthermore, the discretizations derived using the mixed formulation are shown to be asymptotically dual consistent. Numerical results from a simple test problem demonstrate that the dual consistent and asymptotically dual consistent schemes are superior both in terms of solution accuracy and output accuracy.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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