Applications of a moving finite element method

The moving finite element method (MFEM) with polynomial approximations of a ny degree is applied to a variety of models described by partial differenti al equations (PDEs) of the type Gu(t) = Fu(xx) + H, a less than or equal to x less than or equal to b, t greater than or equal to 0, G and F are full matrices. The objective of this work is to show that the proposed formulati on of MFEM is a powerful tool to compute the numerical solution of time-dep endent PDEs involving steep moving fronts. A strategy to choose the penalty constants was devised in relation with the ODE solver tolerances to improv e the robustness of the method. Numerical results concerning combustion mod el, boundary layer problem, catalytic reactor and pressurization of adsorpt ion beds illustrate the effectiveness of our scheme. (C) 2001 Elsevier Scie nce B.V. All rights reserved.