High Quality Content by WIKIPEDIA articles! In mathematics, the Trefftz method is a method for the numerical solution of partial differential equations named after the German mathematician Erich Trefftz (1888-1937). It falls within the class of finite element methods.The hybrid Trefftz finite element method has been considerably advanced since its introduction about 30 years ago. The conventional method of finite element analysis involves converting the differential equation that governs the problem into a variational functional from which element nodal properties - known as field variables - can be found. This can be solved by substituting in approximate solutions to the differential equation and generating the finite element stiffness matrix which is combined with all the elements in the continuum to obtain the global stiffness matrix. Application of the relevant boundary conditions to this global matrix, and the subsequent solution of the field variables rounds off the mathematical process, following which numerical computations can be used to solve real life engineering problems .