High-precision numerical simulation with autoadaptative grid technique in nonlinear thermal diffusion

This paper reports that many engineering problems concern the determination of a steady state solution in the case with strong thermal gradients, and results obtained using the finite-element technique are sometimes inaccurate, particularly for nonlinear problems with unadapted meshes. Building on previous results in linear problems, we propose an autoadaptive technique for nonlinear cases that uses quasi-Newtonian iterations to reevaluate an interpolation error estimation. The authors perfected an automatic refinement technique to solve the nonlinear thermal problem of temperature calculus in a cast-iron cylinder head of a diesel engine