This paper deals with a spherically symmetric three-dimensional inverse heat conduction problem of determining the internal surface temperature distribution of a hollow sphere from the measured data at a fixed location inside it. This is an ill-posed problem, i.e., the solution (if it exists)...

The paper consists of three parts. In the first part, we investigate a posteriori error estimates for the Stokes and Navier–Stokes equations on two-dimensional polygonal domains. Special attention is paid to the sources of the constants in the estimates, as these play a crucial role in...

Error indicators based on solution gradients, interpolation errors, and a posteriori error estimates are presented for use in defining monitor functions for the r-adaptive finite element methods based on moving mesh partial differential equations. The methods are compared with a careful...

The paper is concerned with a posteriori error estimates needed for the adaptive construction of a space grid in solving an initial-boundary value one-dimensional problem for a nonlinear parabolic partial differential equation by the method of lines. A posteriori error indicators are introduced...

An immersed finite element space is used to solve the elliptic interface problems by a finite volume element method. Special nodal basis functions are introduced in a triangle whose interior intersects with the interface so that the jump conditions across the interface are satisfied. Optimal...