Abstract
This work presents an application of the hp- finite
element formulation to solve the general non-linear heat
conduction problem in a solid for cases involving heat
sources and non-linear boundary conditions terms. The
temperature field is semi-discretized in space with
hierarchical basis functions formed using the orthogonal
Legendre polynomials. The good approximation properties
of the hp-finite element method are achieved here by the
combined effect of the traditional mesh refinement
together with the p-extension of the polynomial basis.
Because the temperature field is continuous, the
hp-formulation performs very well. The calculated
temperature field converges much faster in the hp-version
than the traditional h-refinement. In general, the
h-refinement is used for regions with non-smooth solution
and the p-extension for the smooth ones. This work also
shows a systematic way to treat source terms and the
possible non-linear natural boundary conditions present
in the heat conduction equation by including them in the
force vector of the discretized heat conduction equation.
| Original language | English |
|---|---|
| Pages (from-to) | 75-86 |
| Journal | Rakenteiden Mekaniikka |
| Volume | 29 |
| Issue number | 3-4 |
| Publication status | Published - 1996 |
| MoE publication type | D1 Article in a trade journal |