### A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems

Josef Dalík (1991)

Applications of Mathematics

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A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation $-\u03f5{u}^{n}+p{u}^{\text{'}}+qu=f$ are presented and analyzed theoretically. The positive number $\u03f5$ is supposed to be much less than the discretization step and the values of $\left|p\right|,q$. An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.