A posteriori error estimates of krylov subspace approximations to matrix functions

A Posteriori Error Estimates for Finite Volume Approximations

We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and...

On Krylov Subspace Approximations to Thematrix Exponential

A Posteriori Estimates Using Auxiliary Subspace Techniques

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determin...

On A Posteriori Error Estimates

Consider a sequence {xn}n—Q in a normed space X converging to some x* £ X. It is shown that the sequence satisfies a condition of the type ||x* -x„|| < oi||xn xn_¡\\ for some constant a and every n > 1, if the associated null sequence {e„}„=q, en = x* — xn, is uniformly decreasing in norm or if it is alternating with respect to any ordering whose cone of positive elements is acute.

A Posteriori Error Estimates 3

This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations , namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency of this method is shown by numerical ex...