Adaptive remeshing for compressible flow computations
Journal of Computational Physics
On the convergence of finite-element approximations of a relaxed variational problem
SIAM Journal on Numerical Analysis
Numerical approximation of the solution of variational problem with a double well potential
SIAM Journal on Numerical Analysis
Optimal triangular mesh generation by coordinate transformation
SIAM Journal on Scientific and Statistical Computing
Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions
SIAM Journal on Numerical Analysis
First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Delaunay mesh generation governed by metric specifications. Part I algorithms
Finite Elements in Analysis and Design
Delaunay mesh generation governed by metric specifications. Part II. applications
Finite Elements in Analysis and Design
A Variational Method in Image Recovery
SIAM Journal on Numerical Analysis
A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems
SIAM Journal on Numerical Analysis
A New Finite Element Gradient Recovery Method: Superconvergence Property
SIAM Journal on Scientific Computing
Metric tensors for anisotropic mesh generation
Journal of Computational Physics
Mesh Generation: Application to Finite Elements
Mesh Generation: Application to Finite Elements
Journal of Computational Physics
Journal of Computational Physics
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It has been amply demonstrated that anisotropic mesh adaptation can significantly improve computational efficiency over isotropic mesh adaptation especially for problems with strong anisotropic features. Although numerous research has been done on isotropic mesh adaptation for finite element solution of variational problems, little work has been done on anisotropic mesh adaptation. In this paper we consider anisotropic mesh adaptation method for the finite element solution of variational problems. A bound for the first variation of a general functional is derived, which is semi-a posteriori in the sense that it involves the residual and edge jump, both dependent on the computed solution, as well as the Hessian of the exact solution. A formula for the metric tensor M for use in anisotropic mesh adaptation is defined such that the bound is minimized on a mesh that is uniform in the metric specified by M (i.e., an M-uniform mesh). Interestingly, when restricted to isotropic meshes, we can obtain a similar but completely a posteriori bound and the corresponding formula for the metric tensor. When M is defined, an anisotropic adaptive mesh is generated as an M-uniform mesh. Numerical results demonstrate that the new mesh adaptation method is comparable in performance with existing ones based on interpolation error and has the advantage that the resulting mesh also adapts to changes in the structure of the underlying problem.