In this paper we derive optimal a priori L∞(L2) error estimates for mixed finite element displacement formulations of the acoustic wave equation. The computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure. However, the displacemen...

In this paper we provide an a priori error analysis for parabolic optimal control problems with a pointwise (Dirac type) control in space on three dimensional domains. The two dimensional case was treated in [30], however the three dimensional case is technically much more involved. To approximate the problem we use standard continuous piecewise linear elements in space and piecewise constant d...

In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect...

Single-wavelength anomalous dispersion (SAS) data can in principle be phased by direct methods since a priori estimates of the three-phase structure invariants can be computed from these data. The mean phase error of the most reliable triple estimates for a small protein, however, is typically no better than 60 degrees, and does not bode well for applications to larger structures. A procedure i...

In this paper we consider a parabolic optimal control problem with a pointwise (Dirac type) control in space, but variable in time, in two space dimensions. To approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous Galerkin method in time. Despite low regularity of the state equation, we show almost optimal h2 + k ...

It is well known that finite element solutions for elliptic PDEs with Dirac measures as source terms converge, due to the fact that the solution is not in H1, suboptimal in classical norms. A standard remedy is to use graded meshes, then quasioptimality, i.e., optimal up to a log-factor, for low order finite elements can be recovered, e.g., in the L2-norm. Here we show for the lowest order case...

Galerkin approximations to solutions of a Cauchy-Dirichlet problem governed by the generalized porous medium equation

We discuss the error analysis for a moving-boundary system in two phases arising from modeling the penetration of a sharp carbonation front into unsaturated cement-based materials. The special feature of this problem is that the moving boundary is driven by a kinetic condition proportional to the rate of a fast carbonation reaction concentrated on the moving boundary. We prove a priori error es...

This paper is concerned with a priori error estimates for the piecewise linear nite element approximation of the classical obstacle problem. We demonstrate by means of two onedimensional counterexamples that the L2-error between the exact solution u and the nite element approximation uh is typically not of order two even if the exact solution is in H 2(Ω) and an estimate of the form ‖u − uh‖H1 ...

We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In contrast to many results in numerical analysis of optimization problems subject to semilinear parabolic equations, we assume weak second order sufficient conditions. Relying on the resulting quadratic growth condition of th...