TY - JOUR
AU - Morin, Pedro
AB - In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of partial differential equations. As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite-element methods using Lagrange finite elements of any polynomial degree are obtained.
TI - Convergence rates for adaptive finite elements
JF - IMA Journal of Numerical Analysis
DO - 10.1093/imanum/drn039
DA - 2008-07-30
UR - https://www.deepdyve.com/lp/oxford-university-press/convergence-rates-for-adaptive-finite-elements-4URWi6TEhk
SP - 917
EP - 936
VL - 29
IS - 4
DP - DeepDyve
ER -