Geodesic
On a semi-variational method for parabolic equations. I
Applications of Mathematics, Tome 17 (1972) no. 5, pp. 327-351
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The paper aims at a further development of the finite element method, when applied to mixed problems for parabolic equations. Much work has been done on a special Galerkin-type procedure of order $\tau^2$, which is similar to the Crank-Nicholson finite-difference scheme. Here a sequence of approximations is presented, possessing an increasing accuracy in the time increment $\tau$. The first approximation coincides with the above-mentioned procedure. For the second approximation, the rate of convergence $\tau^4$ and the stability with respect to the initial condition is proved. The efficiency of the first and second approximations are compared on a numerical example.
The paper aims at a further development of the finite element method, when applied to mixed problems for parabolic equations. Much work has been done on a special Galerkin-type procedure of order $\tau^2$, which is similar to the Crank-Nicholson finite-difference scheme. Here a sequence of approximations is presented, possessing an increasing accuracy in the time increment $\tau$. The first approximation coincides with the above-mentioned procedure. For the second approximation, the rate of convergence $\tau^4$ and the stability with respect to the initial condition is proved. The efficiency of the first and second approximations are compared on a numerical example.
DOI : 10.21136/AM.1972.103427
Classification : 35K99, 65M15, 65M99, 65N30 
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Hlaváček, Ivan. On a semi-variational method for parabolic equations. I. Applications of Mathematics, Tome 17 (1972) no. 5, pp. 327-351. doi: 10.21136/AM.1972.103427

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