Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case
We develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In...
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| Format: | Report |
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2004
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| _version_ | 1797074795320311808 |
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| author | Houston, P Robson, J Suli, E |
| author_facet | Houston, P Robson, J Suli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | We develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p. |
| first_indexed | 2024-03-06T23:41:23Z |
| format | Report |
| id | oxford-uuid:6f6ed566-9809-4147-be98-bf7856aa58e9 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:41:23Z |
| publishDate | 2004 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:6f6ed566-9809-4147-be98-bf7856aa58e92022-03-26T19:30:37ZDiscontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar caseReporthttp://purl.org/coar/resource_type/c_93fcuuid:6f6ed566-9809-4147-be98-bf7856aa58e9Mathematical Institute - ePrintsUnspecified2004Houston, PRobson, JSuli, EWe develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p. |
| spellingShingle | Houston, P Robson, J Suli, E Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case |
| title | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case |
| title_full | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case |
| title_fullStr | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case |
| title_full_unstemmed | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case |
| title_short | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case |
| title_sort | discontinuous galerkin finite element approximation of quasilinear elliptic boundary value problems i the scalar case |
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