Error indicators based on solution gradients, interpolation errors, and a posteriori error estimates are presented for use in deening monitor functions for the r-adaptive nite element methods based on moving mesh partial diierential equations. The methods are compared with a careful selection of examples. The numerical results show that the methods based on both interpolation errors and a poste...

In this contribution we derive a posteriori error estimate for finite volume approximations of nonlinear convection diffusion equations in the L∞(L1)-norm. The problem is discretized implicitly in time by the method of characteristics, and in space by piecewise constant finite volume methods. The analysis is based on a reformulation for finite volume methods. The derived a posteriori error esti...

When numerically solving a set of partial differential equations through a finite element strategy associated with a weak formulation, one usually faces the problem of increasing the accuracy of the solution without adding unnecessary degrees of freedom in non-critical parts of the computational domain. In order to identify these regions, indicators were created which allow their automatic dete...

We first derive convergence and a priori stability, next reliability efficiency of posteriori error indicators for Biot poroelastic model coupled with an elastic in R3, solved by continuous Galerkin scheme (CG) the displacement mixed finite element flow. The system is decoupled fixed stress splitting algorithm. numerical implementation residual based simple, even discretization, but at expense ...

In many application domains, the preferred approaches to the numerical solution of hyperbolic partial differential equations such as conservation laws are formulated as finite difference schemes. While finite difference schemes are amenable to physical interpretation, one disadvantage of finite difference formulations is that it is relatively difficult to derive the so-called goal oriented a po...

We derive a posteriori error estimates in the L∞((0, T ];L∞(Ω)) norm for approximations of solutions to linear parabolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat kernel estimates for linear parabolic problems, we first prove a posteriori bounds in the maximum norm for semidiscrete finite element approximations. We then establish a pos...

Abstract. We derive a posteriori error estimates in the L∞((0, T ];L∞(Ω)) norm for approximations of solutions to linear parabolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat kernel estimates for linear parabolic problems, we first prove a posteriori bounds in the maximum norm for semidiscrete finite element approximations. We then estab...

Residual based a posteriori error estimates for conforming nite element solutions of the incompressible Navier{Stokes equations which are computed with four recently proposed two{level methods are derived. The a posteriori error estimates contain additional terms in comparison to the estimates for the solution obtained by the standard one{level method. The importance of these additional terms i...

In this article, a posteriori error analysis for mixed finite element Galerkin approximations of second order linear hyperbolic equations is discussed. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker’s technique introduced earlier by G. Baker (SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equ...