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It is known that the energy technique for a posteriori error analysis of finite element discretizations of parabolic problems yields suboptimal rates in the norm L1(0; T;L2 (Ω)): In thi...
We unify the formulation and analysis of Galerkin and Runge{Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate sol...
We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge{Kutta Collocation (RK-C) methods and the continuous ...
We derive upper and lower a posteriori estimates for the maximum norm error in nite element solutions of monotone semi-linear equations. The estimates hold for Lagrange elements of any xed order, n...
Fundamental tasks in computer vision include determining the position, orientation and trajectory of a moving camera relative to an observed object or scene. Many such visual tracking algorithms hav...
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-D...
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution.
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hy-pothesis.
We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be t...
Error estimates for emission lines in the hydrogen and helium isosequences
Over 35 million surface observations covering the world ocean from 1870–1976 have been processed for the purpose of calculating monthly normals and standard errors of the eastward and northward compon...
In this paper, the linear finite element approximation to the positive and symmetric, linear hyperbolic systems is analyzed and an $O(h^2)$ order error estimate is established under the conditions of ...
In this paper, we provide a theoretical analysis of the partition of unity finite element method(PUFEM), which belongs to the family of meshfree methods. The usual error analysis only shows the orde...
We examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\Cal O(h^2)$ for $d<2q$ and nonuniform triangulations. For ...
This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many d...

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