Biconvergence for Projection Methods via Variational Principles
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In Chapter 2, we formulated linear operator equations in variational form which we then approximated by projection methods. In an entirely analogous manner, we were able to apply projection methods to nonlinear problems. The prototype examples for illustrating our methods were examples of boundary-value problems in ordinary and partial differential equations already introduced in Chapter 1; the convergence analysis for the finite-difference approximations of these examples was the topic of the preceding chapter.
KeywordsVariational Principle Projection Method Variational Equation Convergence Analysis Truncation Error
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References (cf. also References in Chapter 2)
- Aubin (1972,1979), Babuska & Aziz (1972)*, Ciarlet (1978), Ciarlet, Schultz & Varga (1967)*, Douglas & Dupont (1974)*, Fairweather (1978), Kantorovich & Akilov (1964), Krasnoselskii, Vainikko et al. (1972), Lions & Magenes (1972), Mitchell & Wait (1977), Oden & Reddy (1976), Stummel (1970,1972,1976a,1976b,1977)*.Google Scholar