On Petrov-galerkin Formulations for the Linear Hyperbolic Equation
نویسنده
چکیده
We consider conforming Petrov-Galerkin formulations for the advective and advec-tive-diiusive equations. For the linear hyperbolic equation, the continuous formulation is set up using diierent spaces and the discretization follows with diierent \bubble" enrichments for the test and trial spaces. Boundary conditions for residual-free bubbles are modiied to accommodate with the rst order equation case and regular bubbles are used to enrich the other space. Using piecewise linears with these enrichments, the nal formulations are shown to be equivalent to the SUPG method, provided the data is assumed to be piecewise constant. Generalization to include diiusion is also presented.
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