Adaptive wavelet frame domain decomposition methods for nonlinear elliptic equations

作者：Lellek Dominik^*

来源：Numerical Methods for Partial Differential Equations, 2013, 29(1): 297-319.

DOI：10.1002/num.21713

• adaptivity
• additive Schwarz method
• nonlinear approximation
• nonlinear elliptic boundary value problems
• wavelet frames
• overlapping domain decomposition

In this article, we are concerned with the numerical treatment of nonlinear elliptic boundary value problems. Our method of choice is a domain decomposition strategy. Partially following the lines from (Cohen, Dahmen and deVore, SIAM J Numer Anal 41 (2003), 1785-1823; Kappei, Appl Anal J Sci 90 (2011), 1323-1353; Lui, SIAM J Sci Comput 21 (2000), 1506-1523; Stevenson and Werner, Math Comp 78 (2009), 619-644), we develop an adaptive additive Schwarz method using wavelet frames. We show that the method converges with an asymptotically optimal rate and support our theoretical results with numerical tests in one and two space dimensions.

• 出版日期2013-1