Geodesic
Alternating direction Galerkin method for quasilinear parabolic equations
Mathematica Applicanda, Tome 7 (1979) no. 15, pp. 5-23 Cet article a éte moissonné depuis la source Annales Societatis Mathematicae Polonae Series

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Consider the following parabolic equation: (1) ∂u/∂t−∑2i=1(d/dxi)ai(x,t,u,D1u,D2u)+a0(x,t,u,D1u,D2u)=f(x,t), x=(x1,x2)∈Ω⊂R2, t∈[0,T], with the initial value condition u(x,0)=u0(x), x∈Ω, and with the boundary value condition u(x,t)=0, x∈∂Ω, t∈[0,T]. For the solution of equation (1) the author proposes a variational-difference method. Namely, he approximates equation (1) by Galerkin's method with respect to the variables x1,x2 and by the finite-difference method with respect to the variable t. Under some assumptions concerning the coefficients ai, i=0,1,2, an estimate of the error is given.
DOI : 10.14708/ma.v7i15.1476
Classification : 65N30
Mots-clés : Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 
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     author = {M. Dryja},
     title = {Alternating direction {Galerkin} method for quasilinear parabolic equations},
     journal = {Mathematica Applicanda},
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     year = {1979},
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     doi = {10.14708/ma.v7i15.1476},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v7i15.1476/}
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M. Dryja. Alternating direction Galerkin method for quasilinear parabolic equations. Mathematica Applicanda, Tome 7 (1979) no. 15, pp.  5-23. doi: 10.14708/ma.v7i15.1476

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