An anisotropic mesh adaptation method for elliptic PDEs based on hierarchical a posteriori error estimates, solved with a few symmetric Gauss-Seidel sweeps, attains accuracy comparable to Hessian recovery on standard benchmarks.
A posteriori error analysis for finite element solution of elliptic differential equations using equidistributing meshes
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abstract
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.
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A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
An anisotropic mesh adaptation method for elliptic PDEs based on hierarchical a posteriori error estimates, solved with a few symmetric Gauss-Seidel sweeps, attains accuracy comparable to Hessian recovery on standard benchmarks.