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تسجيل مستخدم جديدSecond order splitting for a class of fourth order equations
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We formulate a well-posedness and approximation theory for a class of generalised saddle point problems. In this way we develop an approach to a class of fourth order elliptic partial differential equations using the idea of splitting into coupled second order equations. Our main motivation is to treat certain fourth order surface equations arising in the modelling of biomembranes but the approach may be applied more generally. In particular, we are interested in equations with non-smooth right hand sides and operators which have non-trivial kernels.The theory for well posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments.
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We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with po
int constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments.
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