Error estimation and time-space parameters optimization for FEM non-linear computation

TL;DR: An a posteriori error estimate is derived for the numerical approximation of the solution of a system modeling the flow of two incompressible and immiscible fluids in a porous medium using a large class of conforming, vertex-centered finite volume-type discretizations with fully implicit time stepping.

TL;DR: A new strict upper bound of the error is proposed which separates the contribution of the iterative solver and the contribution to the discretization of the finite element method solved with a non-overlapping domain decomposition method.

TL;DR: In this article, the quality of the numerical solution is assessed by the way in which the constitutive relations are satisfied, and a comparison of the error of the estimator with different estimators drawn from the literature is presented.

TL;DR: In this paper, an extension to the Ladeveze estimator on the constitutive relation was presented, which can lead to a significant improvement in the effectivity indexes in the case of anisotropic meshes.

TL;DR: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.

TL;DR: Statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models as mentioned in this paper, and the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy.

TL;DR: It is shown that an extremely high rate of convergence is reached in practical problems using p-convergent methods, and applications to realistic stress analysis and potential problems are presented.

TL;DR: The Elasticite Reference Record (ER) was created on 2004-09-07, modified on 2016-08-08 as mentioned in this paper, and was used for the first time in 2015.