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Full-Text Articles in Physical Sciences and Mathematics
Analysis Of The Truncation Error And Barrier-Function Technique For A Bakhvalov-Type Mesh, Thái Ahn Nhan, Relja Vulanović
Analysis Of The Truncation Error And Barrier-Function Technique For A Bakhvalov-Type Mesh, Thái Ahn Nhan, Relja Vulanović
Mathematics and Computer Science
We use a barrier-function technique to prove the parameter-uniform convergence for singularly perturbed convection-diffusion problems discretized on a Bakhvalov-type mesh. This is the first proof of this kind in the research literature, the barrier-function approach having only been applied so far to Shishkin-type meshes.
A Note On A Generalized Shishkin-Type Mesh, Thái Ahn Nhan, Relja Vulanović
A Note On A Generalized Shishkin-Type Mesh, Thái Ahn Nhan, Relja Vulanović
Mathematics and Computer Science
The one-dimensional linear singularly perturbed convection-diffusion problem is discretized using the upwind scheme on a mesh which is a mild generalization of Shishkin-type meshes. The generalized mesh uses the transition point of the Shishkin mesh, but it does not require any structure of its fine and course parts. Convergence uniform in the perturbation parameter is proved by the barrier-function technique, which, because of the unstructured mesh, does not rely on any mesh-generating function. In this way, the technical requirements needed in the existing barrier-function approaches are simplified.
Uniform Convergence On A Bakhvalov-Type Mesh Using The Preconditioningapproach. Technical Report, Thái Ahn Nhan, Relja Vulanović
Uniform Convergence On A Bakhvalov-Type Mesh Using The Preconditioningapproach. Technical Report, Thái Ahn Nhan, Relja Vulanović
Mathematics and Computer Science
The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh is analyzed. The preconditioning technique is used to obtain the pointwise convergence uniform in the perturbation parameter.