AbstractThe paper considers a finite‐element discretization for solving two distributed parameter system optimal control problems. Linear and quadratic finite‐element approximations are used in conjunction with Galerkin's method. The first problem involves heating a massive body in a furnace and takes into account furnace dyanmics. The input (fuel flow rate) is magnitude constrained, and the performance index is the terminal cost. The second problem pertains to a plug‐flow heat exchanger and is solved for end‐point control and control along the entire heat exchanger. Uniform wall flux and wall temperature serve as the control variables. The results are compared with earlier results, and advantages of the present approach are di