Mixed Finite Element Methods as Finite Difference Methods for Solving Elliptic Equations on Triangular Elements

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dc.contributor.authorArbogast, Todden_US
dc.contributor.authorDawson, Clinten_US
dc.contributor.authorKeenan, Philen_US
dc.date.accessioned2018-06-18T17:41:12Zen_US
dc.date.available2018-06-18T17:41:12Zen_US
dc.date.issued1993-11en_US
dc.date.noteNovember 1993en_US
dc.description.abstractSeveral procedures of mixed finite element type for solving elliptic partial differential equations are presented. The efficient implementation of these approaches using the lowest-order Raviart-Thomas approximating spaces defined on triangular elements is discussed. A quadrature rule is given which reduces a mixed method to a finite difference method on triangles. This approach substantially reduces the complexity of the mixed finite element matrix, but may also lead to a loss of accuracy in the solution. An enhancement of this method is derived which combines numerical quadrature with Lagrange multipliers on certain element edges. The enhanced method regains the accuracy of the solution, with little additional cost if the geometry is sufficiently smooth. Numerical examples in two dimensions are given comparing the accuracy of the various methods.en_US
dc.format.extent20 ppen_US
dc.identifier.citationArbogast, Todd, Dawson, Clint and Keenan, Phil. "Mixed Finite Element Methods as Finite Difference Methods for Solving Elliptic Equations on Triangular Elements." (1993) <a href="https://hdl.handle.net/1911/101820">https://hdl.handle.net/1911/101820</a>.en_US
dc.identifier.digitalTR93-53en_US
dc.identifier.urihttps://hdl.handle.net/1911/101820en_US
dc.language.isoengen_US
dc.titleMixed Finite Element Methods as Finite Difference Methods for Solving Elliptic Equations on Triangular Elementsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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