TY - JOUR
T1 - Convergence and Complexity of Adaptive Finite Element Methods for Elliptic Partial Differential Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 615
EP - 640
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/704.html
KW - Adaptive finite element, convergence, complexity, eigenvalue, nonlinear, nonsymmetric, unbounded.
AB - <p style="text-align: justify;">In this paper, we study adaptive finite element approximations in a
perturbation framework, which makes use of the existing adaptive finite element
analysis of a linear symmetric elliptic problem. We analyze the convergence
and complexity of adaptive finite element methods for a class of elliptic partial
differential equations when the initial finite element mesh is sufficiently fine.
For illustration, we apply the general approach to obtain the convergence and
complexity of adaptive finite element methods for a nonsymmetric problem, a
nonlinear problem as well as an unbounded coefficient eigenvalue problem.</p>