The combination technique for a two-dimensional convection-diffusion problem with exponential layers

Franz, Sebastian; Liu, Fang; Roos, Hans–Görg; Stynes, Martin; Zhou, Aihui

doi:10.1007/s10492-009-0013-9

Cited by 9 publications

(7 citation statements)

References 29 publications

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“…For the two-scale interpolation error (I N N , N E−I N,N E) the results of [6] remain valid (Lemma 2.3 and 2.4, modified for the reaction-diffusion problem). For the two-scale projection error an estimate in L 2 and L ∞ is easy.…”

Section: Supercloseness and A Combination Techniquementioning

confidence: 70%

“…Next we present an application of the supercloseness result to the combination technique. We analyse the version of the combination technique presented in [6], for a different version see [14]. Remark that in [15] the authors observe numerically a nice behaviour of a combination technique in the balanced norm.…”

Section: Supercloseness and A Combination Techniquementioning

confidence: 99%

“…We obtain the same accuracy as on a N × N mesh with less degrees of freedom. In the following we use the notation of [6].…”

Section: Supercloseness and A Combination Techniquementioning

confidence: 99%

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Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

Roos¹

2016

Preprint

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Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H 1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss also anisotropic problems, semilinear equations, supercloseness and a combination technique.

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Section: Supercloseness and A Combination Techniquementioning

confidence: 70%

Section: Supercloseness and A Combination Techniquementioning

confidence: 99%

See 1 more Smart Citation

Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

Roos¹

2016

Preprint

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show abstract

“…Next we present an application of the supercloseness result to the combination technique. We analyse the version of the combination technique presented in [1].…”

mentioning

confidence: 99%

“…We obtain the same accuracy as on a N × N mesh with less degrees of freedom. In the following we use the notation of [1].…”

mentioning

confidence: 99%

Error Estimates in Balanced Norms of Finite Element Methods on Shishkin Meshes for Reaction-Diﬀusion Problems

Ханс-Гёрг¹

2016

Model. anal. inf. sist.

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A Multiscale Sparse Grid Technique for a Two-Dimensional Convection-Diffusion Problem with Exponential Layers

Russell

Madden

2015

Lecture Notes in Computational Science and Engineering

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The combination technique for a two-dimensional convection-diffusion problem with exponential layers

Cited by 9 publications

References 29 publications

Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

Error Estimates in Balanced Norms of Finite Element Methods on Shishkin Meshes for Reaction-Diﬀusion Problems

A Multiscale Sparse Grid Technique for a Two-Dimensional Convection-Diffusion Problem with Exponential Layers

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