Numerical solution of fully nonlinear elliptic equations by Böhmer�s method

• Autores: Oleg Davydov, Abid Saeed
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 254, Nº 1, 2013 (Ejemplar dedicado a: Nonlinear Elliptic Differential Equations, Bifurcation, Local Dynamics of Parabolic Systems and Numerical Methods), págs. 43-54
• Idioma: inglés
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• Resumen

  • We present an implementation of Böhmer�s finite element method for fully nonlinear elliptic partial differential equations on convex polygonal domains, based on a modified Argyris element and Bernstein�Bézier techniques. Our numerical experiments for several test problems, involving the classical Monge�Ampère equation and an unconditionally elliptic equation, confirm the convergence and error bounds predicted by Böhmer�s theoretical results.