Abstract
We continue the study of semilinear elliptic BVPs of the form
where Ω is a bounded open domain in RN, N = 2, and f is a nonlinear function of x and u. We will deal with f ≡ up, –u + up, or variants thereof. We wish to compute numerical solutions of (12.1) by BEMand plot their graphics for visualization. on domains with various geometries and topologies. We also hope to survey existing algorithms and to introduce new ones, set certain numerical benchmarks, and explore singular perturbation cases. This chapter is based mainly on our prior work [37].
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Chen, G., Chen, G., Zhou, J. (2010). Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (II): Algorithms and Computations for Unstable Solutions from Various Models. In: Boundary Element Methods with Applications to Nonlinear Problems. Atlantis Studies in Mathematics for Engineering and Science, vol 7. Atlantis Press. https://doi.org/10.2991/978-94-91216-27-5_12
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DOI: https://doi.org/10.2991/978-94-91216-27-5_12
Publisher Name: Atlantis Press
Online ISBN: 978-94-91216-27-5
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