Computation of Morse decompositions for semilinear elliptic PDEs
Michael W. Smiley, Changbum Chun · Numerical Methods for Partial Differential Equations · 2001
Abstract A numerical method for computing all solutions of an elliptic boundary value problem Au + g[u, λ] = 0 and their Morse indices as steady‐states of the parabolic problem ut + Au + g[u, λ] = 0 is presented. Morse decompositions are also determined. The method uses a finite element approach that is based on the method of alternative problems. Error estimates for the finite element approximations are verified and examples are given. © John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 290–312, 2001