ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We consider solutions z of the Cauchy-problem for hyperbolic Euler-Lagrange equations derived from a general Lagrangian f(x, y, z; zx, zy) in two independent variables x, y. z is supposed to be an extremal of the corresponding variational problem. Visualizing z as a surface in R3 we give a geometric interpretation of Lewy's well-known characteristic approximation scheme for the numerical solution of second order hyperbolic equations by approximating z via a polyhedral construction built up from subunits which consist of two characteristic triangles having one side in common but lying on different planes in R3. Utilizing ideas from Cartan-geometry one can (in an appropriate sense) introduce the “mean curvature” of these subunits and it is seen that this curvature vanishes (up to terms of higher order). That is a highly plausible result for the polyhedral approximation of “minimal surfaces”.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670040131