Trefftz functions for the non-stationary problems

Different types of Trefftz functions for non-stationary linear and weakly nonlinear differential equations are presented. The Trefftz methods are defined and briefly described. Certain results for non-stationary problems of heat conduction (among others boundary temperature identification and thermal diffusivity estimation), for beam vibration, for thermoelasticity and for the wave equation (direct and inverse problem of membrane vibrations) are shown. In many cases, the FEM with Trefftz functions (FEMT) as probe functions is applied. Three kinds of FEMT are tested for direct and inverse non-stationary problems. Examples of the making use of T-functions for solving inverse problems and smoothing inaccurate input data are discussed.