. " implicit constitutive theory" . " numerical methods" . " nonlinear partial differential equations" . "V\u00FDvoj a systematick\u00E1 matematick\u00E1 anal\u00FDza materi\u00E1lov\u00FDch model\u016F v mechanice kontinua zalo\u017Een\u00FDch na nov\u011B navr\u017Een\u00E9 implicitn\u00ED konstitutivn\u00ED teorii a n\u00E1vrh p\u0159esn\u00FDch, spolehliv\u00FDch, efektivn\u00EDch a robustn\u00EDch numerick\u00FDch metod pro po\u010D\u00EDta\u010Dov\u00E9 simulace chov\u00E1n\u00ED takov\u00FDchto materi\u00E1l\u016F. Prozkoum\u00E1n\u00ED mo\u017Enost\u00ED, omezen\u00ED a p\u0159\u00EDpadn\u00FDch roz\u0161\u00ED\u0159en\u00ED implicitn\u00ED konstitutivn\u00ED teorie a p\u0159idru\u017Een\u00FDch p\u0159\u00EDstup\u016F jako\u017Eto n\u00E1stroje pro n\u00E1vrh termodynamicky konzistentn\u00EDch materi\u00E1lov\u00FDch model\u016F v mechanice kontinua. Zkoum\u00E1n\u00ED nov\u00FDch p\u0159\u00EDstup\u016F ke kvalitativn\u00ED anal\u00FDze syst\u00E9m\u016F parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic popisuj\u00EDc\u00EDch chov\u00E1n\u00ED materi\u00E1l\u016F s implicitn\u00EDmi konstitutivn\u00EDmi vztahy (ot\u00E1zka definice \u0159e\u0161en\u00ED, existence \u0159e\u0161en\u00ED a jeho kvalitativn\u00EDch vlastnosti) se z\u0159etelem k vyu\u017Eitelnosti takov\u00FDchto metod p\u0159i v\u00FDpo\u010Dtech aproximativn\u00EDho \u0159e\u0161en\u00ED numerick\u00FDmi metodami (lok\u00E1ln\u00ED a posteriori odhady p\u0159edpokl\u00E1daj\u00EDc\u00ED zahrnut\u00ED algebraick\u00E9 slo\u017Eky chyby) a k mo\u017En\u00E9 rigor\u00F3zn\u00ED redukci model\u016F na spojit\u00E9 \u00FArovni. Anal\u00FDza itera\u010Dn\u00EDch metod pro kone\u010Dn\u011Bdimension\u00E1ln\u00ED syst\u00E9my algebraick\u00FDch rovnic vznikl\u00FDch diskretizac\u00ED dan\u00FDch soustav neline\u00E1rn\u00EDch parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic a to s d\u016Frazem na zahrnut\u00ED algebraick\u00E9 chyby (chyba vznikl\u00E1 p\u0159i \u0159e\u0161en\u00ED line\u00E1rn\u00EDch soustav) do a posteriorn\u00EDch odhad\u016F chyby. Anal\u00FDza Krylov itera\u010Dn\u00EDch metod jako\u017Eto n\u00E1stroje pro rigor\u00F3zn\u00ED redukci modelu na diskr\u00E9tn\u00ED \u00FArovni. Spojen\u00ED uveden\u00FDch p\u0159\u00EDstup\u016F s c\u00EDlem z\u00EDskat p\u0159esn\u00FD a vy\u010D\u00EDsliteln\u00FD celkov\u00FD odhad chyby p\u0159i numerick\u00FDch simulac\u00EDch a na z\u00E1klad\u011B tohoto odhadu navrhnout optim\u00E1ln\u00ED numerick\u00E9 techniky pro rozs\u00E1hl\u00E9 numerick\u00E9 simulace v aplikovan\u00FDch v\u011Bdn\u00EDch discipl\u00EDn\u00E1ch." . " model reduction" . . . "mathematical modeling" . . " a posteriori error analysis" . "2015-02-16+01:00"^^ . . . "Implicitly constituted material models: from theory through model reduction to efficient numerical methods"@en . . . . "20"^^ . "20"^^ . "http://www.isvav.cz/projectDetail.do?rowId=LL1202"^^ . . " numerical stability" . . "0"^^ . . " fluid and solid mechanics" . "Development and systematic mathematical analysis of material models in continuum mechanics that are based on the novel implicit constitutive theory. Development of accurate, reliable, efficient and robust numerical methods for computer simulations of such materials. Investigation of features, drawbacks and possible extensions of the implicit constitutive theory and related concepts as the theoretical tool for development of thermodynamically consistent material models in continuum mechanics. Investigation of new approaches to mathematical analysis of nonlinear systems of partial differential equations describing the behaviour of materials with implicit consittutive relations (suitable definition of solution, existence of a solution and its qualitative properties) with regard to applicability of such approaches to the search of an approximate solution using numerical methods (local a posteriori error estimates assuming inclusion of algebraic errors) and to rigorous model reduction on the continuous level. Analysis of iterative algorithms for finite dimensional systems of algebraic equations arising from the discretization of such nonlinear partial differential equations with a special emphasis on algebraic errors (inevitable errors arising for example in iterative linear algebraic solvers) and their incorporation into a posteriori error estimates. Analysis of Krylov subspace methods as tools for rigorous model reduction on the discrete level. Combination of these approaches will aim at accurate and computable estimate of the total error in the numerical simulations, and, on the basis of this estimate, design of optimal numerical techniques for large-scale numerical simulations in applied sciences."@en . "1"^^ . . "2017-08-31+02:00"^^ . . "2012-09-01+02:00"^^ . . "0"^^ . . "Materi\u00E1ly s implicitn\u00EDmi konstitutivn\u00EDmi vztahy: Od teorie p\u0159es redukci model\u016F k efektivn\u00EDm numerick\u00FDm metod\u00E1m" . . . "2014-01-31+01:00"^^ . "LL1202" . "mathematical modeling; fluid and solid mechanics; implicit constitutive theory; nonlinear partial differential equations; model reduction; numerical methods; numerical stability; a posteriori error analysis; stopping criteria"@en . .