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In this article, the details of new hybrid methods have been presented to solve systems of ordinary differential equations (ODEs). These methods are based on backward differentiation formulae (BDF) where one additional stage point (or off-step point) and two step points have been used in the first derivative of the solution to improve the absolute stability regions compared with some existing methods...
We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity...
In this note, we extend our studies on finite element Galerkin schemes for elliptic variational inequalities of first to the one of second kind. Especially we perform the corresponding a posteriori error analysis for a simple friction problem and a model flow of a Bingham fluid. Collecting the experiences from these examples, we propose a framework for deriving a posteriori error estimates for a certain...
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