APPROXIMATION OF NONLINEAR PARABOLIC EQUATIONS USING A FAMILY OF CONFORMAL AND NON-CONFORMAL SCHEMES

作者：Eymard Robert^*; Handlovicova Angela; Mikula Karol

来源：Communications on Pure and Applied Analysis, 2012, 11(1): 147-172.

DOI：10.3934/cpaa.2012.11.147

• Conformal finite element scheme
• non-conformal finite element scheme
• finite volume scheme
• convergence of the scheme
• nonlinear parabolic equation

We consider a family of space discretisations for the approximation of nonlinear parabolic equations, such as the regularised mean curvature flow level set equation, using semi-implicit or fully implicit time schemes. The approximate solution provided by such a scheme is shown to converge thanks to compactness and monotony arguments. Numerical examples show the accuracy of the method.

• 出版日期2012-1