A. Rieder, A DOMAIN EMBEDDING METHOD FOR DIRICHLET PROBLEMS IN ARBITRARY SPACE DIMENSION, Modelisation mathematique et analyse numerique, 32(4), 1998, pp. 405-431
An embedding method for the discretization of Dirichlet boundary value
problems over general domains in arbitrary space dimension is propose
d. The main advantage of the method lies in the use of Cartesian coord
inates independent of the underlying domain. Error estimates and aspec
ts of the numerical realization are considered. To obtain an efficient
solver for the resulting linear system of equations an easy-to-use pr
econditioning is recommended and analyzed. A variety of numerical expe
riments illustrate and confirm the theoretical results. (C) Elsevier,
Paris.