A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices
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This paper describes the use of an a posteriori error estimator to control anisotropic mesh adaptation for computing inviscid compressible flows. The a posteriori error estimator and the coupling strategy with an anisotropic remesher are first introduced. ...
An anisotropic a posteriori error estimate is derived for a finite element discretization of the wave equation in two space dimensions. Only the error due to space discretization is considered, and the error estimates are derived in the nonnatural L-2(0, T ...
In this paper we aim at controlling physically meaningful quantities with emphasis on environmental applications. This is carried out by an efficient numerical procedure combining the goal-oriented framework [R. Becker, R. Rannacher, An optimal control app ...
We present a technique for the rapid and reliable prediction of linear-functional outputs of coercive and non-coercive linear elliptic partial differential equations with affine parameter dependence. The essential components are: (i) rapidly convergent glo ...
In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution-dependent (Online) calculation of the exponential-i ...
Moving from the anisotropic interpolation error estimates derived in Formaggia and Perotto, (2001), we provide here both a-priori and a-posteriori estimates for a generic elliptic problem. The a-priori result is deduced by following the standard finite ele ...
A posteriori error estimates for the heat equation in two space dimensions are presented. A classical discretization is used, Euler backward in time, and continuous, piecewise linear triangular finite elements in space. The error is bounded above and below ...
In this paper we propose a new technique to obtain upper and lower bounds on the energy norm of the error in the velocity field, for the Stokes problem. It relies on a splitting of the velocity error in two contributions: a projection error, that quantifie ...
In this Note we derive a posteriori error estimates for a multiscale method, the so-called heterogeneous multiscale method, applied to elliptic homogenization problems. The multiscale method is based on a macro-to-micro formulation. The macroscopic method ...
We compute solutions of solutal phase-field models for dendritic growth of an isothermal binary alloy using anisotropic mesh refinement techniques. The adaptive strategy is based on anisotropic a posteriori estimators using a superconvergent recovery techn ...
