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Uniform error estimates for general semilinear turning point problems on layer-adapted meshes (1701.06323v1)
Published 23 Jan 2017 in math.NA
Abstract: We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The problem is discretized using higher order finite elements on suitable constructed layer-adapted meshes. Finally, error estimates uniform with respect to the singular perturbation parameter $\varepsilon$ are proven in the energy norm.