Author(s)

V. Sladek, J. Sladek & Ch. Zhang

Abstract

The paper deals with the numerical solution of initial-boundary value problems for diffusion equation with variable coefficients by using a local weak formulation and a meshless approximation of spatial variations of the field variable. The time variation is treated either by the Laplace transform technique or by the linear Lagrange interpolation in the time stepping approach. Advanced formulation for local integral equations is employed. A comparative study of numerical results obtained by the Laplace transform and the time stepping approach is given in a test example for which the exact solution is available and utilized as a benchmark solution. Keywords: transient heat conduction, weak formulation, Laplace transform, time stepping, accuracy, computational efficiency. 1 Introduction The diffusion and the transient heat conduction problems in functionally graded materials belong to frequent engineering problems. From the mathematical point of view, the solution of initial-boundary value problems for the diffusion equation with variable coefficients is rather complex task and therefore there is a demand to have sophisticated and efficient numerical techniques. The local weak formulations appear to be appropriate. The local integral equations replacing the governing equations are acceptable from the physical point of view, since such equations express the balance principles. The variation of material coefficients is involved naturally without any complication as compared with the formulations

Keywords

transient heat conduction, weak formulation, Laplace transform, time stepping, accuracy, computational efficiency