{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:49:35Z","timestamp":1776840575434,"version":"3.51.2"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,2,15]],"date-time":"2007-02-15T00:00:00Z","timestamp":1171497600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2007,2,28]]},"DOI":"10.1007\/s11075-007-9066-6","type":"journal-article","created":{"date-parts":[[2007,2,14]],"date-time":"2007-02-14T14:49:58Z","timestamp":1171464598000},"page":"355-383","source":"Crossref","is-referenced-by-count":9,"title":["A fully discrete H 1-Galerkin method with quadrature for nonlinear advection\u2013diffusion\u2013reaction equations"],"prefix":"10.1007","volume":"43","author":[{"given":"M.","family":"Ganesh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Mustapha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,2,15]]},"reference":[{"key":"9066_CR1","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1002\/num.20122","volume":"22","author":"R. Aitbayev","year":"2006","unstructured":"Aitbayev, R.: Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem. Numer. Methods Partial Differ. Equ. 22, 847\u2013866 (2006)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"9066_CR2","unstructured":"Aitbayev, R.: Convergence analysis of a quadrature finite element Galerkin scheme for a biharmonic problem. IMA J. Numer. Anal. (to appear)"},{"key":"9066_CR3","first-page":"229","volume":"327","author":"G. Baker","year":"1973","unstructured":"Baker, G.: Simplified proofs of error estimates for the least squares method for Dirichlet\u2019s problem. Math. Comput. 327, 229\u2013235 (1973)","journal-title":"Math. Comput."},{"key":"9066_CR4","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1002\/cpa.3160230408","volume":"23","author":"J. Bramble","year":"1970","unstructured":"Bramble, J., Schatz, A.: Rayleigh\u2013Ritz\u2013Galerkin methods for Dirichlet\u2019s problem using subspaces without boundary conditions. Commun. Pure Appl. Math. 23, 653\u2013675 (1970)","journal-title":"Commun. Pure Appl. Math."},{"key":"9066_CR5","first-page":"1","volume":"25","author":"J. Bramble","year":"1971","unstructured":"Bramble, J., Schatz, A.: Least-squares methods for 2mth order elliptic boundary value problems. Math. Comput. 25, 1\u201332 (1971)","journal-title":"Math. Comput."},{"key":"9066_CR6","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1093\/imanum\/24.1.157","volume":"24","author":"B. Bialecki","year":"2004","unstructured":"Bialecki, B., Ganesh, M., Mustapha, K.: A Petrov-Galerkin method with quadrature for elliptic boundary value problems. IMA J. Numer. Anal. 24, 157\u2013177 (2004)","journal-title":"IMA J. Numer. Anal."},{"key":"9066_CR7","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0377-0427(00)00509-4","volume":"128","author":"B. Bialecki","year":"2001","unstructured":"Bialecki, B., Fairweather, G.: Orthogonal spline collocation methods for partial differential equations. J. Comput. Appl. Math. 128, 55\u201385 (2001)","journal-title":"J. Comput. Appl. Math."},{"key":"9066_CR8","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1002\/mma.1670020416","volume":"2","author":"H. Blum","year":"1980","unstructured":"Blum, H., Rannacher, R.:On the boundary value problem of the biharmonic operator on domains with angular corners. Math. Methods Appl. Sci. 2, 556\u2013581 (1980)","journal-title":"Math. Methods Appl. Sci."},{"key":"9066_CR9","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)"},{"key":"9066_CR10","volume-title":"Lecture Notes in Math, vol. 385","author":"J. Douglas","year":"1974","unstructured":"Douglas, J., Dupont, T.: Collocation method for parabolic equations in a single variable. In: Lecture Notes in Math, vol. 385. Springer, Berlin Heidelberg New York (1974)"},{"key":"9066_CR11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1051\/m2an\/1977110100031","volume":"11","author":"J. Douglas","year":"1977","unstructured":"Douglas, J., Dupont, T., Rachford, H.H., Wheeler, M.F.: Local H \u20131 Galerkin and adjoint local H \u20131 Galerkin procedures for elliptic equations. RAIRO Anal. Numer. 11, 3\u201312 (1977)","journal-title":"RAIRO Anal. Numer."},{"key":"9066_CR12","volume-title":"Lecture Notes in Pure and Applied Mathematics, vol. 34","author":"G. Fairweather","year":"1978","unstructured":"Fairweather, G.: Finite element Galerkin methods for differential equations. In: Lecture Notes in Pure and Applied Mathematics, vol. 34. Marcel Dekker, New York (1978)"},{"key":"9066_CR13","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1006\/jath.2000.3506","volume":"107","author":"R. Grigorieff","year":"2000","unstructured":"Grigorieff, R., Sloan, I.H., Brandts, J.H.: Superapproximation and commutator properties of discrete orthogonal projections for continuous splines. J. Approx. Theory 107, 244\u2013267 (2000)","journal-title":"J. Approx. Theory"},{"key":"9066_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-96379-7","volume-title":"Elliptic Partial Differential Equations of Second Order","author":"D. Gilbarg","year":"1977","unstructured":"Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer, Berlin Heidelberg New York (1977)"},{"key":"9066_CR15","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/11567646_25","volume":"3752","author":"Y. He","year":"2005","unstructured":"He, Y., Jin, M., Gu, X., Qin, H.: A $\\mathcal{C}$ globally interpolatory spline of arbitrary topology. Lect. Notes Comput. Sci. 3752, 295\u2013306 (2005)","journal-title":"Lect. Notes Comput. Sci."},{"key":"9066_CR16","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1007\/s11390-006-0232-4","volume":"21","author":"Y. He","year":"2006","unstructured":"He, Y., Gu, X., Qin, H.: Automatic shape control of triangular B-splines of arbitrary topology. J. Comput. Sci. Technol. 21, 232\u2013237 (2006)","journal-title":"J. Comput. Sci. Technol."},{"key":"9066_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-11490-8","volume-title":"Elliptic Differential Equations, Theory and Numerical Treatment","author":"W. Hackbusch","year":"1992","unstructured":"Hackbusch, W.: Elliptic Differential Equations, Theory and Numerical Treatment. Springer, Berlin Heidelberg New York (1992)"},{"key":"9066_CR18","volume-title":"Linear and Quasilinear Elliptic Equations","author":"O. Ladyzhenskaya","year":"1968","unstructured":"Ladyzhenskaya, O., Uraltseva, N.: Linear and Quasilinear Elliptic Equations. Academic, New York (1968)"},{"key":"9066_CR19","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1002\/num.20123","volume":"22","author":"N. Ma","year":"2006","unstructured":"Ma, N., Lu, T., Yang, D.: Analysis of incompressible miscible displacement in porous media by characteristics collocation method. Numer. Methods Partial Differ. Equ. 22, 797\u2013814 (2006)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"9066_CR20","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1137\/0717050","volume":"17","author":"P. Percell","year":"1980","unstructured":"Percell, P., Wheeler, M.F.: A $\\mathcal C^1$ finite element collocation method for elliptic equations. SIAM J. Numer. Anal. 17, 605\u2013622 (1980)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9066-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-007-9066-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9066-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:08Z","timestamp":1559365688000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-007-9066-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,15]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,2,28]]}},"alternative-id":["9066"],"URL":"https:\/\/doi.org\/10.1007\/s11075-007-9066-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,15]]}}}