Liu, W.B. and Barrett, J. (1993) Finite-Element Approximation of The P-Laplacian. Mathematics of Computation, 61 (204). pp. 523-537. ISSN 0025-5718 .
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In this paper we consider the continuous piecewise linear finite element approximation of the following problem: Given p is-an-element-of (1, infinity), f, and g , find u such that -del . (\delu\p-2delu) = f in OMEGA subset-of R2, u = g on partial derivative OMEGA. The finite element approximation is defined over OMEGA(h), a union of regular triangles, yielding a polygonal approximation to OMEGA. For sufficiently regular solutions u, achievable for a subclass of data f, g, and OMEGA, we prove optimal error bounds for this approximation in the norm W1,q (OMEGA(h)) , q = p for p < 2 and q is-an-element-of [1,2] for p > 2, under the additional assumption that OMEGA(h) subset-or-equal-to OMEGA. Numerical results demonstrating these bounds are also presented.
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Social Sciences > Kent Business School|
|Depositing User:||Steve Wenbin Liu|
|Date Deposited:||05 Oct 2009 16:58|
|Last Modified:||05 Oct 2009 16:58|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/22907 (The current URI for this page, for reference purposes)|
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