Adaptive energy preserving methods for partial differential equations |
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Authors: | Sølve Eidnes Brynjulf Owren Torbjørn Ringholm |
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Institution: | 1.Department of Mathematical Sciences,Norwegian University of Science and Technology,Trondheim,Norway |
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Abstract: | A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of unity methods, thereby including finite element methods. The schemes are then extended to accommodate r-, h- and p-adaptivity. To illustrate the ideas, the method is applied to the Korteweg–de Vries equation and the sine-Gordon equation. Results from numerical experiments are presented. |
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