A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. (English) Zbl 1159.65353
Summary: For the lowest order Raviart-Thomas mixed finite element, we derive an a posteriori error estimator that provides actual, guaranteed computable upper bounds on the error in the flux variable regardless of jumps in the material coefficients across interfaces. Moreover, the estimator is efficient in that it provides a local lower bound on the error up to a constant that is independent of the solution and the local mesh-size. The estimator may be evaluated at virtually no additional cost compared to the evaluation of the finite element approximation itself.
MSC:
65N15 | Error bounds for boundary value problems involving PDEs |
35J25 | Boundary value problems for second-order elliptic equations |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
35Q60 | PDEs in connection with optics and electromagnetic theory |
65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |