A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used as test functions in one coordinate direction and are combin...
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| creator | Hegarty, Alan F O'Riordan, Eugene |
| description | A Petrov-Galerkin finite element method is constructed for a singularly
perturbed elliptic problem in two space dimensions. The solution contains a
regular boundary layer and two characteristic boundary layers. Exponential
splines are used as test functions in one coordinate direction and are combined
with bilinear trial functions defined on a Shishkin mesh. The resulting
numerical method is shown to be a stable parameter-uniform numerical method
that achieves a higher order of convergence compared to upwinding on the same
mesh. |
| doi_str_mv | 10.48550/arxiv.2311.00554 |
| format | Article |
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perturbed elliptic problem in two space dimensions. The solution contains a
regular boundary layer and two characteristic boundary layers. Exponential
splines are used as test functions in one coordinate direction and are combined
with bilinear trial functions defined on a Shishkin mesh. The resulting
numerical method is shown to be a stable parameter-uniform numerical method
that achieves a higher order of convergence compared to upwinding on the same
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perturbed elliptic problem in two space dimensions. The solution contains a
regular boundary layer and two characteristic boundary layers. Exponential
splines are used as test functions in one coordinate direction and are combined
with bilinear trial functions defined on a Shishkin mesh. The resulting
numerical method is shown to be a stable parameter-uniform numerical method
that achieves a higher order of convergence compared to upwinding on the same
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perturbed elliptic problem in two space dimensions. The solution contains a
regular boundary layer and two characteristic boundary layers. Exponential
splines are used as test functions in one coordinate direction and are combined
with bilinear trial functions defined on a Shishkin mesh. The resulting
numerical method is shown to be a stable parameter-uniform numerical method
that achieves a higher order of convergence compared to upwinding on the same
mesh.</abstract><doi>10.48550/arxiv.2311.00554</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers |
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