Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Posteriori Error Estimators for the Raviart--Thomas Element
SIAM Journal on Numerical Analysis
A posteriori error estimate for the mixed finite element method
Mathematics of Computation
hp-Approximation Theory for BDFM and RT Finite Elements on Quadrilaterals
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements
SIAM Journal on Scientific Computing
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
Hi-index | 31.45 |
The present work provides a straightforward and focused set of tools and corresponding theoretical support for the implementation of an adaptive high order finite element code with guaranteed error control for the approximation of elliptic problems in mixed form. The work contains: details of the discretisation using non-uniform order mixed finite elements of arbitrarily high order; a new local post-processing scheme for the primary variable; the use of the post-processing scheme in the derivation of new, fully computable bounds for the error in the flux variable; and, an hp-adaptive refinement strategy based on the a posteriori error estimator. Numerical examples are presented illustrating the results obtained when the procedure is applied to a challenging problem involving a ten-pole electric motor with singularities arising from both geometric features and discontinuities in material properties. The procedure is shown to be capable of producing high accuracy numerical approximations with relatively modest numbers of unknowns.