Alternating direction Galerkin method for quasilinear parabolic equations

M. Dryja. "Alternating direction Galerkin method for quasilinear parabolic equations." Mathematica Applicanda 7.15 (1979): null. <http://eudml.org/doc/293343>.

@article{M1979,
abstract = {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.},
author = {M. Dryja},
journal = {Mathematica Applicanda},
keywords = {Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods},
language = {eng},
number = {15},
pages = {null},
title = {Alternating direction Galerkin method for quasilinear parabolic equations},
url = {http://eudml.org/doc/293343},
volume = {7},
year = {1979},
}

TY - JOUR
AU - M. Dryja
TI - Alternating direction Galerkin method for quasilinear parabolic equations
JO - Mathematica Applicanda
PY - 1979
VL - 7
IS - 15
SP - null
AB - 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.
LA - eng
KW - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
UR - http://eudml.org/doc/293343
ER -