Uniform error estimates for general semilinear turning point problems on\n layer-adapted meshes

2017/01/23 by Simon Becher, Becher, Simon
Computer Science · Mathematics · #65L11 #65L50 #65L60 #65L70 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1701.06323

openalex publication_date 2017/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a singularly perturbed semilinear boundary value problem of a\ngeneral form that allows various types of turning points. A solution\ndecomposition is derived that separates the potential exponential boundary\nlayer terms. The problem is discretized using higher order finite elements on\nsuitable constructed layer-adapted meshes. Finally, error estimates uniform\nwith respect to the singular perturbation parameter \ε are proven in\nthe energy norm.\n

Related

• Uniform Norm Error Estimates for 2D Turning Point Problem
• Parameter-uniform fitted mesh higher order finite difference scheme for singularly perturbed problem with an interior turning point
• Finite Element Error Estimates for Critical Growth Semilinear Problems without Angle Conditions
• Piecewise equidistant meshes for quasilinear turning point problems: Technical report
• Cut finite element error estimates for a class of nonlinear elliptic PDEs