Keywords: hp-adaptive finite element method, heat and moisture transfer, interfacing finite element solvers.

Nowadays, several numerical methods are used for the analysis of various engineering problems. The most popular is the finite element method. Any result obtained by a numerical method should be accompanied by an error estimate which is unfortunately often missing. This contribution describes an effort to obtain both results and error estimates with minimum modifications of existing computer codes.

The effort is based on the HERMES computer code which is devoted to the hp-adaptive finite element method and on the TRFEL code which deals with transport processes. HERMES starts an analysis with a very coarse mesh of finite elements and usually linear approximation functions. Later with respect to error estimates, it refines the mesh and it increases the degree of approximation polynomials. It also enables adaptive methods to be applied within the time integration. TRFEL has been intended as a part of larger open source code. TRFEL deals with transport processes such as heat, moisture, salt and coupled transfer. It enables the solution of one, two and three dimensional problems which are either stationary or non-stationary. There is a large library of material (constitutive) models.

The two computer codes described have been connected with the aid of an interface. The conductivity matrices of particular finite elements become a matrix-matrix product where the matrix of gradients and the matrix of material parameters occur. The matrix of gradients is assembled in HERMES because it depends on the mesh and on the approximation functions used. The matrix of material parameters is assembled in TRFEL. It means that HERMES has to send to TRFEL the number of integration points of an element, the coordinates of the integration points and the actual values of the approximated variables at the integration points. On the other hand, TRFEL assembles the matrix of material parameters and sends it to HERMES. Then, HERMES assembles the conductivity matrix, the vector of the right hand side, it solves the system of linear equations and computes the error estimates.

The connection of the two computer codes was tested on the preliminary examples of non-stationary heat transfer through a concrete wall exposed to fire. Combination of adaptive methods in HEMRES and material models implemented in the TRFEL code leads to suitable finite element meshes. More realistic problems can be solved in the future.

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