D. J. Estep, M. G. Larson, and R. D. Williams, Estimating the error of numerical solutions of systems of reaction-di#usion equations, Memoirs A.M.S., 146 (2000), pp. 1--109. Home/Search Document Not in Database Summary Related Articles Check |
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Generalized Green's Functions and the Effective Domain of.. - Estep, Holst, Larson (2002) Self-citation (Estep Larson) (Correct)
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D. J. Estep, M. G. Larson, and R. D. Williams, Estimating the error of numerical solutions of systems of reaction-di#usion equations, Memoirs A.M.S., 146 (2000), pp. 1--109.
Accounting for Stability: A Posteriori Error Estimates.. - Estep, Holst, Mikulencak (2001) Self-citation (Estep) (Correct)
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D. Estep, M. Larson, and R. Williams, Estimating the error of numerical solutions of systems of reaction-di#usion equations, Mem. Amer. Math. Soc, 696 (2000), pp. 1--109.
Using Krylov-Subspace Iterations in Discontinuous Galerkin.. - Estep, Freund Self-citation (Estep) (Correct)
....of (1) called the discontinuous Galerkin method (dG method) see, e.g. 2,3,10] and the references given there. The reason for employing space time finite element methods is to take advantage of the new approach to computational error estimation based on residuals and variational analysis; see [3,4]. Let q 1 be an integer. The dG(q) method uses discontinuous (in time) approximations that are piecewise polynomials of degree at most q in time and piecewise linear polynomials in space. The approximations are allowed to be discontinuous at the time nodes, but for fixed time, they are continuous ....
....we evaluate the integrals involving some form of mass matrix, i.e. U i ; v i ) Gamma [U i ] n Gamma1 ; v i Delta , and (f i (U) v i ) using the lumped mass, or composite trapezoidal rule, quadrature. The choice of this quadrature rule is dictated by stability considerations; see [4]. Equations (3) defining the dG(q) approximation result in a large sparse system of nonlinear equations that needs to be solved on each space time slab Sn . For this task, we use an inexact Newton method combined with preconditioned Krylov subspace iterations to obtain an approximate solution of ....
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Estep, D., Larson, M., Williams, R.: Estimating the error of numerical solutions of systems of reaction-diffusion equations. Mem. Amer. Math. Soc., 1999, to appear
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