Finite element solution of nonlinear elliptic problems
Numerische Mathematik
Convergence of Adaptive Finite Element Methods
SIAM Review
Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
SIAM Journal on Numerical Analysis
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The gradient theory for the surface tension of simple fluids and mixtures is rigorously analyzed based on mathematical theory. The finite element approximation of surface tension is developed and analyzed, and moreover, an adaptive finite element method based on a physical-based estimator is proposed and it can be coupled efficiently with Newton's method as well. The numerical tests are carried out both to verify the proposed theory and to demonstrate the efficiency of the proposed method.