Numerical solution of field problems by nonconforming Taylor discretization

An algorithm for the numerical solution of field problems is presented. The method is based on expanding the unknown function in a Taylor series about some nodal points so that the coefficients of the series for the various nodes are considered as unknowns. Discrepancy between the values resulting from Taylor expansions about distinct nodes is allowed if it is on the same order of magnitude as the estimated error resulting from the discretization. This enables considerable savings in computation effort in addition to the advantage of specifying the accuracy of the obtained solution. Geometrical flexibility, which enables handling complex boundaries for a large variety of field problems, is another advantage of the proposed scheme. The algorithm is applied to nonlinear steady-state heat-conduction. A test case is treated numerically, and for the evaluation of the scheme the results are compared with the analytical solution.