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A higher order finite element method with modified graded mesh for singularly perturbed two-parameter problems. (English) Zbl 1455.65121

Summary: This paper presents a modified graded mesh for singularly perturbed two-parameter problems. The mesh is generated recursively using Newton’s algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on higher order polynomials of degree \(p \geq 1\). We prove parameter uniform convergence of optimal order in \(\varepsilon \)-weighted energy norm. A test example is taken to compare the proposed graded mesh with others found in the literature.

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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