Validation of error estimators and superconvergence by a computer-based approach

Abstract

In this work a computer-based methodology for studying the asymptotic properties of the finite element solution in the interior of grids of triangles is presented. This methodology is applied to numerically analyze the robustness of error estimators first for patchwise uniform grids and then for general grids of the type used in practical engineering computations. The same methodology is also employed to determine the points of superconvergence for the scalar heat conduction problem for patchwise uniform meshes. The energy impact of air infiltration on a house was measured by performing a series of tests on the house under various operating modes. The tests were done for three house conditions, house with preliminary tightening and covered windows, house with attic insulated and covered windows, and finally, with windows uncovered. Three types of tests were conducted: tests of unheated house operating under natural conditions, tests of heated house operating under natural conditions and tests of heated house operating under pressurized/de-pressurized conditions obtained by controlled variation of air flow rates and air flow directions. The program STAM developed by Liu [1992] to implement the Short Term Average Measurement method for determining the building thermal parameters was II if modified to suit the test house and test methodology specic to this study. The soundness of the STAM program was checked by feeding the program synthetic hourly internal temperature data and measured values of incident solar radiation, outdoor temperature, air flow rate and heat input. The synthetic temperature data was generated by applying the measured variables to two different electric networks representative of heat flows in the test house. It was found that STAM is a robust program that was independent of the building type and which was able to satisfactorily I reproduce values of the building parameters used to generate the synthetic data. The following observations were made based on experiments on the test house: (a)The phenomenon of heat recovery by air leaking through the walls was observed to be a non zero quantity, which suggests that heat recovery effects do exist in real homes. The range of UME values was 0.8 to -0.2. (b)The dependence of heat recovered by leaking air on the rate of air leakage through the walls was Studied and found to be consistent with previous test cell studies. The IHEE values show a tendency to increase with decreasing flow rates. (c)Incident solar radiation has an important effect on the IHEE values, as shown by the difference in these values during summer time and winter time tests. IHEE typically increased by 0.5 when flow switched froi-n pressurization to depressurization during periods with average solar radiation levels of 200 W/m2 . The same flow reversal caused IHEE changes of 0. 1-0.2 when average radiation levels were 60 W/m 2 d) The direction of air leakage has a large impact on the IHEE values when solar radiation is present. The set of experiments done in the framework of this study shows that, for the heating season, de-pressurization is more beneficial than pressurizing the house. (e)The tracer gas results show that for low house pressurization or de- pressurization it is not possible to achieve a pure infiltration or exfiltration mode. In such cases, bi directional air flow can occur which may have an important effect on IFFEE.