The Method of Characteristics with Gradients and integrals
نویسندگان
چکیده
This paper is concerned with the Cubic Interpolation scheme CIP proposed by T. Yabe for the Galerkin Characteristic Method and the possibility of improving the precision of PDE solvers when the differentiated form of the equation is used. For convection diffusion equations a Lagrangian treatment of the convective term is analyzed for various approximations of the projection operator. It is found that indeed it is worthwhile solving the coupled system formed by the PDE and its d-derivatives (in dimension d). A conservative scheme can be constructed by using also the integrated form of the PDE and a bubble correction. Key-words Partial differential equations, Galerkin characteristic method, unstructured mesh, convection diffusion, bubble functions, cubic interpolation.
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