Uniform error estimates for general semilinear turning point problems on layer-adapted meshes
Provides theoretical error bounds for a class of singularly perturbed problems with turning points, which is incremental for numerical analysis of boundary value problems.
The paper proves uniform error estimates for higher-order finite element discretizations of general semilinear turning point problems on layer-adapted meshes, achieving robustness with respect to the singular perturbation parameter.
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.