Nové mincovní nálezy z dolního Podyjí v kontextu raně středověké Moravy

V článku jsou vyhodnoceny nálezy středověkých mincí z konce 10. až počátku 13. stol., které byly v posledním desetiletí učiněny v dolním Podyjí, a to jak při archeologických terénních výzkumech, tak povrchovým průzkumem s pomocí detektoru kovů. Soubor čítající více než 170 mincí je významný pro poznání peněžního oběhu na Moravě v raném středověku. Zejména nálezy jednotlivých mincí byly donedávna vzácné. Pět mincí z polohy Kostice – Zadní hrúd a blízkého okolí pochází z 2. pol. 10. století. Většinou se jedná o ražby datované před r. 976, doposud jediné z oblasti dolního Podyjí a Pomoraví, včetně přilehlé části rakouského Podunají. Nálezy mincí z 1. pol. 11. stol. ukazují na významnou roli uherské mince ve struktuře oběživa na Moravě. Od poloviny 11. stol. nastupují početné mince domácí provenience, ražné především olomouckými Přemyslovci.The article evaluates medieval coins from the end of the tenth century to the beginning of the thirteenth century, found over the past decade in the lower Dyje (Thaya) River region (the southeast part of the Czech Republic) during both terrain excavations and surface surveys with the use of a metal detector. The assemblage of more than 170 coins is an important source for learning about monetary circulation in Moravia at the Early Middle Ages. Finds of individual coins were especially rare until recently. Five coins from the Kostice – Zadní hrúd site and the surrounding area date to the second half of the tenth century. These were mostly coins struck before 976, thus far the only ones from the lower Dyje River and Morava River regions, including adjacent Austrian parts of the Danubian Basin. Coin finds from the first half of the eleventh century indicate the prominent role of Hungarian coins in the structure of currency in Moravia. Numerous coins of domestic provenance, minted mostly by the Olomouc Přemyslids, start appearing in the middle of the 11th century

On Nitsche's method for elastic contact problems

We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilised finite element method for which the error estimates can be obtained with minimal regularity assumptions and without the saturation assumption. We present three different Nitsche's mortaring techniques for the contact boundary each corresponding to a different stabilising term. Our numerical experiments show the robustness of Nitsche's method and corroborates the efficiency of the a posteriori error estimators

Mortaring for linear elasticity using mixed and stabilized finite elements

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the unstabilized mixed mortar method. For simplicity, both methods use a Lagrange multiplier defined on a trace mesh inherited from one side of the interface only. We derive a quasi-optimality estimate for the stabilized method and present the stability criteria of the mixed $P_1-P_1$ approximation. Our numerical results demonstrate the stability and the convergence of the methods for tie contact problems. Moreover, the results show that the mixed method can be successfully extended to three dimensional problems

Nitsche's method for Kirchhoff plates

We introduce a Nitsche's method for the numerical approximation of the Kirchhoff-Love plate equation under general Robin-type boundary conditions. We analyze the method by presenting a priori and a posteriori error estimates in mesh-dependent norms. Several numerical examples are given to validate the approach and demonstrate its properties