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

A posteriori error analysis for finite element solution of elliptic differential equations using equidistributing meshes