an:01322622
Zbl 0932.35064
Leguillon, Dominique; Sanchez-Hubert, Jacqueline; Sanchez-Palencia, ??variste
Model problem of singular perturbation without limit in the space of finite energy and its computation
EN
C. R. Acad. Sci., Paris, S??r. II, Fasc. b, M??c. Phys. Astron. 327, No. 5, 485-492 (1999).
00055708
1999
j
35J30 35B25 65L10
numerical computation; boundary layer; finite elements; singular perturbation
Summary: We consider elliptic problems of singular perturbation which depend on a small parameter \(\varepsilon\), the righ-hand side \(f\) belonging to the dual of the energy space for \(\varepsilon>0\). For \(\varepsilon= 0\), \(f\) belongs neither to the energy space nor to the admissible spaces of Lions and Magenes, taking into account the behaviour at the boundary. We exhibit boundary layer phenomena with large intensity. These boundary layers determine \(u^0(x,\varepsilon)\) (the leading term) which explodes at an order of \(\varepsilon\) depending on \(f\). Numerical computations are faithful only with a very thin mesh in the boundary layers. We also give some results concerning the case when \(f\) can be treated within the framework of Lions and Magenes theory for the limit problem.