Numerical solution of heat conduction problems using orthogonal collocation on finite elements

Technique of orthogonal collocation along with finite elements has been presented to solve the linear and non linear heat conduction problems numerically. Choice of Lagrangian interpolation polynomials as base function has been opted to discretize the trial function. Error analysis has been discussed in terms of element size for both the linear and non linear problems. Proposed technique has been applied on different types of linear and non linear heat conduction problems and the numerical values are plotted using 2D and 3D graphs.