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| An EEP method for post-computation of super-convergent solutions in one-dimensional Galerkin FEM for second order non-self-adjoint Boundary-Value Problem |
| Revised:March 31, 2005 |
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| DOI：10.7511/jslx20072029 |
| KeyWord:Galerkin FEM,non-self-adjoint,one-dimensional problem,super-convergence,element energy projection |
| YUAN Si LIN Yong-jing |
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| Abstract: |
| The present paper extends the Element Energy Projection(EEP) method,which is very successful in Ritz FEM,to the super-convergent computation in Galerkin FEM for second order non-self-adjoint BVP(Boundary Value Problem).In the study of exact elements,it has been shown and proved that,as long as the test functions are constructed using the solution of the adjoint differential equation,the element is bound to produce exact nodal solutions no matter what the trial functions are employed.For approximate elements,it has been found out that the EEP method can well be applied to Galerkin FEM for super-convergent calculation of both solution functions and derivatives at any point on an element in post-processing stage.The proposed method is simple,effective and efficient.A large number of numerical examples consistently show that the accuracy for both solution functions and derivatives so calculated is well comparable to that of the nodal solution values. |
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