Adaptive Pseudo-Transient-Continuation-Galerkin Methods for Semilinear\n Elliptic Partial Differential Equations

2016/07/05 by Mario Amrein, Thomas P. Wihler, Amrein, Mario +1
Engineering · Mathematics · #49M15 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1607.01421

openalex publication_date 2016/07/05 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the application of pseudo-transient-continuation\n(PTC) schemes for the numerical solution of semilinear elliptic partial\ndifferential equations, with possible singular perturbations. We will outline a\nresidual reduction analysis within the framework of general Hilbert spaces,\nand, subsequently, employ the PTC-methodology in the context of finite element\ndiscretizations of semilinear boundary value problems. Our approach combines\nboth a prediction-type PTC-method (for infinite dimensional problems) and an\nadaptive finite element discretization (based on a robust a posteriori residual\nanalysis), thereby leading to a fully adaptive PTC-Galerkin scheme. Numerical\nexperiments underline the robustness and reliability of the proposed approach\nfor different examples.\n

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