|Publication type:||Article in scientific journal|
|Type of review:||Peer review (publication)|
|Title:||Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations|
Wihler, Thomas P.
|Published in:||Numerical Methods for Partial Differential Equations|
|Publisher / Ed. Institution:||Wiley|
|Subjects:||Dynamical system; Steady states|
|Abstract:||In this article, we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations. We will outline a residual reduction analysis within the framework of general Hilbert spaces, and, subsequently, use the PTC-methodology in the context of finite element discretizations of semilinear boundary value problems. Our approach combines both a prediction-type PTC-method (for infinite dimensional problems) and an adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully adaptive PTC -Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different examples.|
|Fulltext version:||Published version|
|License (according to publishing contract):||Licence according to publishing contract|
|Departement:||School of Management and Law|
|Organisational Unit:||Institute for Risk & Insurance (IRI)|
|Appears in collections:||Publikationen School of Management and Law|
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