A Customized Wavelet-Based Hierarchical A Posteriori Error Indicator for Linear and Nonlinear PDES

This paper presents an adaptive method that can be used to improve the finite element solution of a linear or non-linear PDE by indicating the local as well as global errors. This wavelet-based adaptation is based on hierarchical finite element error estimation scheme. The finite element solution of engineering problems is transformed into the multilevel decomposition of wavelet space. The functions of wavelets coefficient are used as an a posteriori error indicator. The error estimations in the present setting do not have any problem due to the complex domain of engineering structures and is applicable in some small region as well as the complete domain. The proposed technique is quite efficient for linear problems like structures with discontinuity as well as non-linear ones such as contact problem.