Method of asymptotic partial decomposition with discontinuous junctions

Method of asymptotic partial decomposition a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures consisting set cylinders) generates some specific interface conditions between three-dimensional one-dimensional parts. In the case heat equation these ensure continuity solution in average normal flux. However computational reasons strong condition may be undesirable. It preferable to replace it by more flexible over cross section. present paper we introduce justify this alternative junction allowing such discontinuity both stationary non-stationary problems. The closeness solutions hybrid dimension problems fully setting is proved. At discrete level, finite volume schemes are considered, an error estimate established. new version MAPDD compared classical one via numerical tests. shows better stability scheme.