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Convergence of finite difference methods for convection–diffusion problems with singular solutions. (English) Zbl 1018.65110

Summary: We are concerned with initial-boundary value problems of convection-diffusion equations in a square, whose solutions have unbounded derivatives near the boundary. By using finite difference approximations with respect to spatial variables and an implicit method with respect to the time variable, it is shown that the numerical solution is convergent if the derivatives go to infinity under proper conditions. Furthermore, the convergence of numerical solution can be accelerated if the mesh points are some functions of equidistant mesh points.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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