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A posteriori error estimates for FEM with violated Galerkin orthogonality. (English) Zbl 1003.65058

The author investigates Petrov-Galerkin discretizations of nonlinear operator equations with linearly stable operators, where the residuals do not belong to the annihilator \(W_h^{\perp}\) of the discrete test space \(W_h\). Conforming and nonconforming methods are considered separately, and for the treatment of the nonconforming situation the concept of elliptic lifting is introduced.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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