Adaptive Wavelet Methods II - Beyond the Elliptic Case

This paper is concerned with the design and analysis of adaptive wavelet methods for systems of operator equations. Its main accomplishment is to extend the range of applicability of the adaptive wavelet based method developed in [?] for symmetric positive definite problems to indefinite or unsymmetric systems of operator equations. This is accomplished by first introducing techniques (such as the least squares formulation developed in [?]) that transform the original (continuous) problem into an equivalent infinite system of equations which is now well-posed in the Euclidean metric. It is then shown how to utilize adaptive techniques to solve the resulting infinite system of equations. This second step requires a significant modification of the ideas from [?]. The main departure from [?] is to develop an iterative scheme that directly applies to the infinite dimensional problem rather than finite subproblems derived from the infinite problem. This rests on an adaptive application of ...

• Type: Journal
• Year: 2002
• Where: FOCM
• Authors: Albert Cohen, Wolfgang Dahmen, Ronald A. DeVore
• Keywords: Adaptive, Adaptive Wavelet, FOCM 2002, Operator Equations