Direct methods in the calculus of variations
Direct methods in the calculus of variations
A comparison of adaptive refinement techniques for elliptic problems
ACM Transactions on Mathematical Software (TOMS)
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Data Oscillation and Convergence of Adaptive FEM
SIAM Journal on Numerical Analysis
Poincaré-Friedrichs Inequalities for Piecewise H1 Functions
SIAM Journal on Numerical Analysis
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
A convergent adaptive finite element method for an optimal design problem
Numerische Mathematik
Linear Convergence of an Adaptive Finite Element Method for the $p$-Laplacian Equation
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
SIAM Journal on Numerical Analysis
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We formulate and analyze an adaptive nonconforming finite element method for the solution of convex variational problems. The class of minimization problems we admit includes highly singular problems for which no Euler-Lagrange equation (or inequality) is available. As a consequence, our arguments only use the structure of the energy functional. We are nevertheless able to prove convergence of an adaptive algorithm, using even refinement indicators that are not reliable error indicators.