  The paper is concerned with the adaptive finite element solution of linear
elliptic differential equations using equidistributing meshes. A strategy is
developed for defining this type of mesh based on residual-based a posteriori
error estimates and rigorously analyzing the convergence of a linear finite
element approximation using them. The existence and computation of
equidistributing meshes and the continuous dependence of the finite element
approximation on mesh are also studied. Numerical results are given to verify
the theoretical findings.
