Optimal L2-error estimates for the semidiscrete Galerkin\ud approximation to a second order linear parabolic initial and\ud boundary value problem with nonsmooth initial data

In this article, we have discussed a priori error estimate for the semidiscrete Galerkin approximation of a general second order parabolic initial and boundary value problem with non-smooth initial data. Our analysis is based on an elementary energy argument without resorting to parabolic duality technique. The proposed technique is also extended to a semidiscrete mixed method for parabolic problems. Optimal L2-error estimate is derived for both cases, when the initial data is in L2

An hp-Local Discontinuous Galerkin method for Parabolic\ud Integro-Differential Equations

In this article, a priori error analysis is discussed for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that the L2 -norm of the gradient and the L2 -norm of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

A priori error estimates for the optimal control of laser surface hardening of steel

A priori error estimates for the optimal control of laser surface hardening of stee

Optimal L2 estimates for semidiscrete Galerkin methods for\ud parabolic integro-differential equations with nonsmooth data

In this article, we discuss an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth initial data. It is based on energy arguments and on a repeated use of time integration, but without using parabolic type duality technique. Optimal L2-error estimate is derived for the semidiscrete approximation, when the initial data is in L2

An a posteriori error analysis of a mixed finite element Galerkin approximation to second order linear parabolic problems

In this article, a posteriori error estimates are derived for a mixed finite element Galerkin approximation to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstruction method, a posteriori error estimates in $L^\infty(L^2)$ and $L^2(L^2)$-norms with optimal order of convergence for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on backward Euler method, a completely discrete scheme is analyzed and a posteriori bounds are derived, which improves earlier results on a posteriori estimates for mixed parabolic problems

Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

Studies of the performance of different front-end systems for flat-panel multi-anode PMTs with CsI(Tl) scintillator arrays

We have studied the performance of two different types of front-end systems for our gamma camera based on Hamamatsu H8500 (flat-panel 64 channels multi-anode PSPMT) with a CsI(Tl) scintillator array. The array consists of 64 pixels of $6\times6\times20{\rm mm}^3$ which corresponds to the anode pixels of H8500. One of the system is based on commercial ASIC chips in order to readout every anode. The others are based on resistive charge divider network between anodes to reduce readout channels. In both systems, each pixel (6mm) was clearly resolved by flood field irradiation of $^{137}$Cs. We also investigated the energy resolution of these systems and showed the performance of the cascade connection of resistive network between some PMTs for large area detectors.Comment: 9 pages, 6 figures, proceedings of the 7th International Workshop on Radiation Imaging Detectors (IWORID7), submitted to NIM

An H<SUP>1</SUP>-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

Optimal error estimates in L2 H1 and H2-norms are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by an H1-Galerkin procedure

Convergence of finite difference method for the generalized solutions of Sobolev equations

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and BrambleHilbert Lemma, a priori error estimates in discrete L2 as well as in discrete H1 norms are derived first for the semidiscrete methods. For the fully discrete schemes, both backward Euler and CrankNicolson methods are discussed and related error analyses are also presented

Numerical methods for hyperbolic and parabolic integro-differential equations

An analysis by energy methods is given for fully discrete numerical methods for time-dependent partial integro-differential equations. Stability and error estimates are derived in H1 and L2. The methods considered pay attention to the storage needs during time-stepping