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Numerical solution of second-order elliptic equations on plane domains. (English) Zbl 0717.65082
The paper presents a general discretization method for linear convective diffusion equations. The schemes are based on an integral formula and have the following properties:
1. They are particularly suited to the case when convection is dominant;
2. Solutions obtained by them satisfy a discrete conservation law;
3. A discrete maximum principle is valid.
The author shows that the finite element solution converges to the exact one with the rate O(h) in \(H^ 1(D)\).

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
Full Text: DOI EuDML
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