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Title: An H-1-Galerkin mixed finite element method or an evolution equation with a positive-type memory term
Authors: PANI, AK
Issue Date: 2002
Citation: SIAM JOURNAL ON NUMERICAL ANALYSIS, 40(4), 1475-1490
Abstract: An H-1-Galerkin mixed finite element method is analyzed for a class of evolution equations with memory. When a classical mixed method is applied to such problems, it has not been possible to obtain any estimate for the flux. However, the proposed approach yields optimal order convergence without the LBB consistency condition and quasi uniformity of the finite element mesh. Compared to the results proved for one space variable, the L-2 estimate of the flux is not optimal for problems in two and three space dimensions. Therefore, a modification of the method is proposed and analyzed. A maximum norm estimate is also derived in one and two space variables. A backward Euler approximation of the modified method is also analyzed.
ISSN: 0036-1429
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