caa a22 4500 378885588 CHVBK 20180305123441.0 cr unu---uuuuu 161128e20040401xx s 000 0 eng 10.1515/1569395041172944 doi (NATIONALLICENCE)gruyter-10.1515/1569395041172944 Li J. Department of Mathematical Sciences, University of Nevada Las Vegas, 4505 Maryland Parkway,Las Vegas, Nevada 89154-4020, USA Optimal uniform convergence analysis for a singularly perturbed quasilinear reaction-diffusion problem [Elektronische Daten] [J. Li] The standard conforming finite element methods on one type of highly nonuniform rectangular meshes are considered for solving the quasilinear singular perturbation problem -ε2(u xx + u yy ) + ƒ(x,y;u) = 0. By using a special interpolation operator and the integral identity technique, optimal uniform convergence rates of O(N -(k+1)) in the L2-norm are obtained for all k-th (k ≥ 1) order conforming tensor-product finite elements, where N is the number of intervals in both x- and y-directions. Hence Apel and Lube's suboptimal results are improved to optimal order and generalized to the quasilinear case. Copyright 2004, Walter de Gruyter finite element method nationallicence singular perturbation nationallicence uniform convergence analysis nationallicence Journal of Numerical Mathematics Walter de Gruyter 12/1(2004-04-01), 39-54 1570-2820 12:1<39 2004 12 jnma https://doi.org/10.1515/1569395041172944 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569395041172944 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Li J. Department of Mathematical Sciences, University of Nevada Las Vegas, 4505 Maryland Parkway,Las Vegas, Nevada 89154-4020, USA NATIONALLICENCE 773 0- Journal of Numerical Mathematics Walter de Gruyter 12/1(2004-04-01), 39-54 1570-2820 12:1<39 2004 12 jnma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter