In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem where A is an elliptic partial-differential operator and is positive, nonincreasing and log-convex on with . Error estimates are derived in the norm of , and some estimates for the first order time derivatives of the errors are also given.
In this paper we consider a parabolic inverse problem in which two unknown functions are involved in the boundary conditions, and attempt to recover these functions by measuring the values of the flux on the boundary. Explicit solutions for the temperature and the radiation terms are derived, and some stability and asymptotic results are discussed. Finally, by using the newly proposed numerical procedure some computational results are presented.
In this paper, we investigate the a priori and the a posteriori error analysis for the finite element approximation to a regularization version of the variational inequality of the second kind. We prove the abstract optimal error estimates in the - and -norms, respectively, and also derive the optimal order error estimate in the -norm under the strongly regular triangulation condition. Moreover, some residual–based a posteriori error estimators are established, which can provide the global upper...
We combine the theory of radial basis functions with the finite difference method to solve the inverse heat problem, and use five standard radial basis functions in the method of the collocation. In addition, using the newly proposed numerical procedure, we also discuss some experimental numerical results.
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