Implicitly constituted material models: from theory through model reduction to efficient numerical methods

The unique features of models arising from the framework of implicit constitutive theory call for careful mathematical analysis and for development of accurate, efficient and robust numerical methods for simulations using the new models. These issues will be addressed in the presented project (see the official project information). It is assumed that the project will substantially influence research activities of the MathMAC centre.

Short description of the project

The nonstandard structure of constitutive relations arising from the new framework requires the reconsideration of many existing approaches in the mathematical theory of partial differential equations and the development of new ones. In particular, basic notions such as the concept of the solution and its well-posedness need to be reconsidered. Further, the complexity of the constitutive relations calls for rigorous investigation on MOdel REduction – the identification of simplified models that capture the chosen (practically relevant) information about the behaviour of the system and disregard irrelevant information. Reliable numerical simulations require the derivation of sharp a posteriori error estimates to control all possible sources of errors, including rarely studied but important algebraic errors.

We believe that in solving difficult problems in mathematical modelling the individual aspects discussed above – physics, mathematical analysis and numerical analysis – are so closely interrelated that no breakthrough can be achieved without emphasising the holistic approach as the main principle. Our vision is to follow this principle: the entire process of MOdelling of complex materials will be REvisited in an innovative manner.

Want to know MORE? See our research plan and meet our research team.

In the case you are interested in our activities, you should follow the seminar which is held within the project.

  • For a complete list of our project publications see the page of our preprints and published work.
  • Recent selected results achieved within the project
    Málek, Josef and Strakoš, Zdeněk: Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs, SIAM, SIAM Spotlight Series, 2015. [URL:]
    [bibtex] [ris]