We establish an a-posteriori error estimate, with corresponding bounds, that is valid for any FOSLS L-minimization problem. Such estimates follow almost immediately from the FOSLS formulation, but they are usually difficult to establish for other methodologies. We present some numerical examples to support our theoretical results. We also establish a local a-priori lower error bound that is use...

We focus ourselves on the analysis of the solution of unsteady linear 2D singularly perturbed convection–diffusion equation. This type of equation can be considered as simplified model problem to many important problems, especially to Navier– Stokes equations. The space discretization of such a problem is a difficult task and it stimulated development of many stabilization methods (e.g. streaml...

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

We present a new error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems. The analysis consists of three steps. First we prove a posteriori estimates for the error in the approximate eigenvectors and eigenvalues. The error in the eigenvectors is measured both in the L' and energy norms. In these estimates the error is bounded in terms of the mesh size, a st...

We present a model for generalized Newtonian fluid flow through a porous medium. In the model the dependence of the fluid viscosity on the velocity is replaced by a dependence on a smoothed (locally averaged) velocity. With appropriate assumptions on the smoothed velocity, existence of a solution to the model is shown. Two examples of smoothing operators are presented in the appendix. A numeric...

In this article we investigate the numerical approximation of coupled Stokes and Darcy fluid flow equations in an axisymmetric domain. The fluid flow is assumed to be axisymmetric. Rewriting the problem in cylindrical coordinates reduces the 3-D problem to a problem in 2-D. This reduction to 2-D requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting w...