Galerkin's Method for Some Highly Nonlinear Problems
Galerkin's method is analyzed for mixed initial value-boundary value problems for the following two equations:$\frac {\partial u}{\partial t} - \sum^n_{i = 1} \frac {\partial}{\partial x_i} A_i(x, \nabla u) = f(x, t, u, \nabla u)$and$\frac {\partial^2 u}{\partial t^2} - \sum^n_{i = 1}\frac {\pa...
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| Veröffentlicht in: | SIAM J. Numer. Anal.; (United States) 1977-04, Vol.14 (2), p.327-347 |
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| container_end_page | 347 |
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| container_title | SIAM J. Numer. Anal.; (United States) |
| container_volume | 14 |
| creator | Dendy, J. E. |
| description | Galerkin's method is analyzed for mixed initial value-boundary value problems for the following two equations:$\frac {\partial u}{\partial t} - \sum^n_{i = 1} \frac {\partial}{\partial x_i} A_i(x, \nabla u) = f(x, t, u, \nabla u)$and$\frac {\partial^2 u}{\partial t^2} - \sum^n_{i = 1}\frac {\partial}{\partial x_i} A_i(x, \nabla u) = f(x, t, u, \nabla u).$Optimal order H1and L2convergence estimates are obtained. |
| doi_str_mv | 10.1137/0714021 |
| format | Article |
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Anal.; (United States)</jtitle><date>1977-04-01</date><risdate>1977</risdate><volume>14</volume><issue>2</issue><spage>327</spage><epage>347</epage><pages>327-347</pages><issn>0036-1429</issn><eissn>1095-7170</eissn><abstract>Galerkin's method is analyzed for mixed initial value-boundary value problems for the following two equations:$\frac {\partial u}{\partial t} - \sum^n_{i = 1} \frac {\partial}{\partial x_i} A_i(x, \nabla u) = f(x, t, u, \nabla u)$and$\frac {\partial^2 u}{\partial t^2} - \sum^n_{i = 1}\frac {\partial}{\partial x_i} A_i(x, \nabla u) = f(x, t, u, \nabla u).$Optimal order H1and L2convergence estimates are obtained.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/0714021</doi><tpages>21</tpages></addata></record> |
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| identifier | ISSN: 0036-1429 |
| ispartof | SIAM J. Numer. Anal.; (United States), 1977-04, Vol.14 (2), p.327-347 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | SIAM Journals Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | 990200 - Mathematics & Computers Application programming interfaces Boundary conditions BOUNDARY-VALUE PROBLEMS Error rates Estimates Estimation methods Galerkin methods GALERKIN-PETROV METHOD GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE Integers ITERATIVE METHODS NONLINEAR PROBLEMS Nonlinearity NUMERICAL SOLUTION Ordinary differential equations Partial differential equations SERIES EXPANSION Sine function |
| title | Galerkin's Method for Some Highly Nonlinear Problems |
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