Analysis of Finite Difference Schemes For Linear Partial Differential Equations with Generalized Solutions

“While there are plenty of books on finite difference (FD) schemes for linear PDE in case of smooth coefficients and inhomogeneous terms, the literature seems lacking when it comes to the nonsmooth case. This monograph fills the gap. … The text addresses graduate students in mathematics and researchers.” (M. Muthsam, Monatshefte für Mathematik, 2016)

“The authors present a new monograph on finite difference schemes for pde’s with weak solutions. … readable for specialist working in the field of numerical analysis, maybe including excellent graduate students of mathematics. … for scientists interested in the analysis of discretization methods for very weak solutions, including solutions in Besov or Bessel-potential spaces, the monography presents many fruitful ideas and useful ingredients.” (H.-G. Roos, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 94 (11), 2014)