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Remarks on a posteriori error estimation for finite element solutions. (English) Zbl 1109.65094
The authors utilize the classical hypercircle method and the lowest order Raviart-Thomas \(H(div)\) element to obtain a posteriori estimates of the \(P_{1}\) finite element solutions for the 2D Poisson equation. A few order estimation methods are also discussed for comparison. Numerical examples are also provided.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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