On the approximation of singular source terms in differential equations. (English) Zbl 0938.65112

The author studies differential equations with singular source terms. For such equations classical convergence results do not apply, as these rely on the regularity of the solution and the source terms. Some elliptic and parabolic problems are studied numerically and theoretically, and it is shown that, with the right approximation of the singular source terms, full convergence order can be achieved away from the singularities, whereas the convergence will be poor in a vicinity of these.
Reviewer: L.G.Vulkov (Russe)


65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35R05 PDEs with low regular coefficients and/or low regular data
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05 Heat equation
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