TITLE

SUPRACONVERGENCE AND SUPERCLOSENESS OF A DISCRETISATION FOR ELLIPTIC THIRD-KIND BOUNDARY-VALUE PROBLEMS ON POLYGONAL DOMAINS

AUTHOR(S)
Emmrich, E.
PUB. DATE
April 2007
SOURCE
Computational Methods in Applied Mathematics;2007, Vol. 7 Issue 2, p135
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The third-kind boundary-value problem for a second-order elliptic equation on a polygonal domain with variable coefficients, mixed derivatives, and first-order terms is approximated by a linear finite element method with first-order accurate quadrature. The corresponding bilinear form does not need to be strongly positive. The discretisation is equivalent to a finite difference scheme. Although the discretisation is in general only first-order consistent, supraconvergence, i.e., convergence of higher order, is shown to take place even on nonuniform grids. Local error estimates of optimal order min(s, 3/2) (with a logarithmic factor if s = 3/2) in the H¹(Ω)-norm are proved for s ∈ (1/2, 2] if the exact solution is in the Sobolev -- Slobodetskij space H1+s(Ω). If neither oblique boundary sections nor mixed derivatives occur, then the optimal order s is achieved. The supraconvergence result is equivalent to the supercloseness of the gradient.
ACCESSION #
25732573

 

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