One of the frequently discussed topics of today is the nature and causes of global warming observed in the last 100-150 years and the prediction of its future development. The answers to these questions are mainly sought using climatic and meteorological models based on the current (imperfect) state-of-the-art about processes in the
atmosphere, hydrosphere and lithosphere. In addition to data from observations proxy data on the climate history over longer periods of time are also used for model calibration. One of the paleoclimatic methods producing proxy data is the reconstruction of the ground surface temperature history from temperature-depth profiles measured in deep boreholes. The lecture will focus on the principles and results of this method.

Fokker–Planck equation is one of the most important tools for investigation of dynamic systems under random excitation. Finite Element Method represents very effective solution possibility particularly when transition processes are investigated or more detailed solution is needed. However, a number of specific problems must be overcome. They follow predominantly from the large multi-dimensionality of the Fokker–Planck equation, shape of the definition domain and usual requirements on the nature of the solution which are out of a conventional practice of the Finite Element employment. Unlike earlier studies it is coming to light that multi-dimensional simplex elements are the most suitable to be deployed. Moreover, new original algorithms for the multi-dimensional mesh generating were developed as well as original procedure of the governing differential and algebraic systems assembling and subsequent analysis. Finally, an illustrative example is presented together with aspects typical for the problem with large multi-dimensionality.

Damage is a phenomenon/concept in continuum mechanics of solid materials undergoing various degradation processes with numerous applications in engineering and in computational mechanics and (geo)physics. Combination with inertial effects may be important modelling issue to prevent various undesired effects otherwise occuring in quasistatic models. Various damage models and their variants as a phase-field fracture will be overviewed. Also, several numerical approaches will be presented, amenable to compute vibrations or waves emitted during fast damage/fracture, together with various extensions of the basic scenario, combining mass or heat transfer, or plasticity.